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reverse","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:           176,            128;\n  1:          2904,           4224,           1536;\n  2:         42592,          92928,          67584,           16384;\n  3:        585640,        1703680,        1858560,          901120,          163840;\n  4:       7730448,       28110720,       40888320,        29736960,        10813440,         1572864;\n  5:      99207416,      432905088,      787100160,       763248640,       416317440,       121110528,       14680064;\n  6:    1247178944,     6349274624,    13852962816,     16791470080,     12211978240,      5328863232,     1291845632,      134217728;\n  7:   15433839432,    89796883968,   228573886464,    332471107584,    302246461440,    175852486656,    63946358784,    13287555072,    1207959552;\n  8:  188635815280,  1234707154560,  3591875358720,   6095303639040,   6649422151680,   4835943383040,  2344699822080,   730815528960,  132875550720,   10737418240;\n  9: 2282493364888, 16599951744640, 54327114800640, 105361677189120, 134096680058880, 117029829869568, 70927169617920, 29476226334720, 8038970818560, 1299227607040, 94489280512;\n","recurrence_sentence":"The row polynomials satisfy (n+1)*P(n,x) = (11*n+22+(8*n+16)*x)*P(n-1,x) for n >= 1, with P(0,x) = 176 + 128*x.","mathematica":"P[0, x_] := 176 + 128*x;\nP[n_, x_] := P[n, x] = Expand[Together[((11*n + 22 + (8*n + 16)*x)*P[n - 1, x])/(n + 1)]];\nTable[CoefficientList[P[n, x], x], {n, 0, 9}] // Flatten","pari":"P(N) = {my(v = vector(N + 1)); v[1] = 176 + 128*x; for(n = 1, N, my(i = n + 1); v[i] = ((11*n + 22 + (8*n + 16)*x)*v[i - 1])/(n + 1)); 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-26633b980c3508e8","steps":["basis A007318","D"],"edges":["e-0566c972c7be0ca0","e-0ec9ff8fdacbcaa0"],"text":"A038226 \u2192 basis A007318 \u2192 D"},"headline":"A038226 \u2192 basis A007318 \u2192 D","chain":null}