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1727002697728,          319277809664;\n  6:     1785793904896,     18488219250688,      83740757782528,      216740784848896,      350610093137920,       362984567013376,       234872366891008,        86843564228608,       14048223625216;\n  7:    60716992766464,    707174386338816,    3660667411636224,    11053780027293696,    21457337700040704,     27768319376523264,     23956981422882816,     13287065326977024,     4298756429316096,      618121839509504;\n  8:  2064377754059776,  26715476817244160,  155578364994539520,   536897887039979520,  1215915803002306560,   1888245717603581952,   2036343420945039360,   1505867403724062720,   730788592983736320,   210161425433231360,    27197360938418176;\n  9: 70188843638032384, 999158832964931584, 6465145389773086720, 25099976219119042560, 64964644331837521920, 117700649730623275008, 152318487886688944128, 140798602248199864320, 91104977925305794560, 39300186556014264320, 10171812990968397824, 1196683881290399744;\n","recurrence_sentence":"The row polynomials satisfy P(n,x) = (34+44*x)*P(n-1,x) for n >= 1, with P(0,x) = 1156 + 2992*x + 1936*x^2.","mathematica":"P[0, x_] := 1156 + 2992*x + 1936*x^2;\nP[n_, x_] := P[n, x] = Expand[(34 + 44*x)*P[n - 1, x]];\nTable[CoefficientList[P[n, x], x], {n, 0, 9}] // Flatten","pari":"P(N) = {my(v = vector(N + 1)); v[1] = 1156 + 2992*x + 1936*x^2; for(n = 1, N, my(i = n + 1); v[i] = (34 + 44*x)*v[i - 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-ec89fb3fc20684fc","steps":["x \u21a6 x/(x+1)","basis A013609"],"edges":["e-492aa71fabef2dc6","e-a332078b6506b7bd"],"text":"A038336 \u2192 x \u21a6 x/(x+1) \u2192 basis A013609"},"headline":"A038336 \u2192 x \u21a6 x/(x+1) \u2192 basis A013609","chain":null}