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0]"}]}],"used_by":[],"used_by_total":0,"links":[],"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:            289,             918,              729;\n  1:           4913,           23409,            37179,             19683;\n  2:          83521,          530604,          1264086,           1338444,            531441;\n  3:        1419857,        11275335,         35815770,          56883870,          45172485,           14348907;\n  4:       24137569,       230016834,        913302135,        1934051580,        2303796735,         1463588514,          387420489;\n  5:      410338673,      4562000541,      21736590813,       57538034505,       91383937155,        87083516583,        46103038191,        10460353203;\n  6:     6975757441,     88633153368,     492696058428,     1565034538536,     3107053863270,      3947786085096,      3135006596988,      1422608035608,       282429536481;\n  7:   118587876497,   1695109058163,   10768928134212,    39908380732668,    95075848216062,    151002817754922,    159885336446388,    108829514724012,     43211719081593,      7625597484987;\n  8:  2015993900449,  32018726654190,  228839722852005,   969203532079080,  2693815699455090,   5134095803667348,   6795126798971490,   6167005834360680,   3672996121935405,   1296351572447790,   205891132094649;\n  9: 34271896307633, 598750188433353, 4754780908147215, 22655132562348495, 71963362256871690, 160012652547632346, 254137742281533726, 288307522756361790, 228950091600640245, 121208872023868365, 38501641701699363, 5559060566555523;\n","recurrence_sentence":"The row polynomials satisfy (1+x)*P(n,x) = (17+44*x+27*x^2)*P(n-1,x) for n >= 1, with P(0,x) = 289 + 918*x + 729*x^2.","mathematica":"P[0, x_] := 289 + 918*x + 729*x^2;\nP[n_, x_] := P[n, x] = Expand[Together[((17 + 44*x + 27*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] = 289 + 918*x + 729*x^2; for(n = 1, N, my(i = n + 1); v[i] = ((17 + 44*x + 27*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-a5302200d285579d","steps":["basis A013609","x \u21a6 x/(x+1)"],"edges":["e-2f341f062a4ee4be","e-948736b3f62d5850"],"text":"A038331 \u2192 basis A013609 \u2192 x \u21a6 x/(x+1)"},"headline":"A038331 \u2192 basis A013609 \u2192 x \u21a6 x/(x+1)","chain":null}