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D","chain":null}},{"id":"l-cdd35584682e3f49","kind":"fingerprint_related","node_a_id":"n-ebafadb809217503","node_b_id":"n-739865e64d311853","fingerprint":"f6-57ca34e86b523c55","oeis_id":null,"in_catalog":null,"target":null,"row_alignment":null,"rows_matched":null,"oeis_nonn":null,"details":{"fingerprint":"f6-57ca34e86b523c55"},"other_id":"n-ebafadb809217503","other":{"id":"n-ebafadb809217503","name":"shift_x_plus_one of basis_map_A013609 of Triangle of coefficients in expansion of (2+3x)^n.","first_index":0,"fingerprint":"f6-57ca34e86b523c55","polytool_family":null,"degree_pattern":"affine","palindromic":0,"gamma_positive":0,"nonnegative":1,"rr_by_factors":1,"preview_rows":[["1"],["11","6"],["121","132","36"]],"card_rows":[["1"],["11","6"],["121","132","36"],["1331","2178","1188","216"]],"row_sums_preview":["1","17","289","4913","83521","1419857","24137569","410338673"],"regions":["(-inf, -1]","(-inf, 0]"],"region_exact":{},"oeis_ids":[],"derivation":{"root":"n-f211cb6153c37c6d","steps":["basis A013610","basis A013609"],"edges":["e-892638ce5a781886","e-1c2af4d858ccc914"],"text":"A027466 \u2192 basis A013610 \u2192 basis A013609"},"headline":"A027466 \u2192 basis A013610 \u2192 basis A013609","chain":null}}],"oeis":[],"bfiles":[],"oeis_texts":[{"oeis_id":"","target":"node","first_row":0,"oeis_offset":0,"reversed":false,"trim_zeros":"none","regular_triangle":false,"rows_shown":10,"polytool_commit":"c48629374597092cc41ef4d6273f37991516f984","triangle_example":"Triangle begins:\n  0:        36,        132,         121;\n  1:       216,       1188,        2178,         1331;\n  2:      1296,       9504,       26136,        31944,         14641;\n  3:      7776,      71280,      261360,       479160,        439230,        161051;\n  4:     46656,     513216,     2352240,      5749920,       7906140,       5797836,       1771561;\n  5:    279936,    3592512,    19758816,     60374160,     110685960,     121754556,      74405562,      19487171;\n  6:   1679616,   24634368,   158070528,    579591936,    1328231520,    1948072896,    1785733488,     935384208,     214358881;\n  7:  10077696,  166281984,  1219401216,   5216327424,   14344900416,   26298984096,   32143202784,   25255373616,   11575379574,    2357947691;\n  8:  60466176, 1108546560,  9145509120,  44711377920,  143449004160,  315587809152,  482148041760,  505107472320,  347261387220,  141476861460,   25937424601;\n  9: 362797056, 7316407296, 67067066880, 368868867840, 1352519182080, 3471465900672, 6364354151232, 8334273293280, 7639750518840, 4668736428180, 1711870023666, 285311670611;\n","recurrence_sentence":"The row polynomials satisfy (1+x)*P(n,x) = (6+17*x+11*x^2)*P(n-1,x) for n >= 1, with P(0,x) = 36 + 132*x + 121*x^2.","mathematica":"P[0, x_] := 36 + 132*x + 121*x^2;\nP[n_, x_] := P[n, x] = Expand[Together[((6 + 17*x + 11*x^2)*P[n - 1, x])/(1 + x)]];\nTable[CoefficientList[P[n, x], x], {n, 0, 9}] // Flatten","pari":"P(N) = {my(v = vector(N + 1)); v[1] = 36 + 132*x + 121*x^2; for(n = 1, N, my(i = n + 1); v[i] = ((6 + 17*x + 11*x^2)*v[i - 1])/(1 + x)); v};\nrow(n, p) = {my(c = Vecrev(p)); c};\nT(N) = {my(v = P(N)); concat(vector(#v, i, row(i - 1, v[i])))};\nT(9)","reading":{"first_row":0,"offset":0,"reversed":false,"trim_zeros":"none","regular_triangle":false}}],"derivation":{"root":"n-bbfc5a54ff13a785","steps":["x \u21a6 x+1","x \u21a6 x/(x+1)"],"edges":["e-7ae18e4d322020fd","e-45bd992a18b3860c"],"text":"A013612 \u2192 x \u21a6 x+1 \u2192 x \u21a6 x/(x+1)"},"headline":"A013612 \u2192 x \u21a6 x+1 \u2192 x \u21a6 x/(x+1)","chain":null}