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1953267757056,     1858815737856,     1081904947200,      391171866624,       84610842624,       9746251776,        429981696;\n  7:    7133863559680,    31788096924672,    62302710767616,    70317639254016,    50188024922112,    23369146859520,     7041093599232,    1305424429056,     131574398976,      5159780352;\n  8:  171432228926464,   856063627161600,  1907285815480320,  2492108430704640,  2109529177620480,  1204512598130688,   467382937190400,  120704461701120,   19581366435840,   1754325319680,    61917364224;\n  9: 4090228109879296, 22629054218293248, 56500199392665600, 83920575881134080, 82239578213253120, 55691570289180672, 26499277158875136, 8813506815590400, 1991623618068480, 287193374392320, 23157094219776, 743008370688;\n","recurrence_sentence":"The row polynomials satisfy (6*n+17+6*x)*P(n,x) = (132*n+506+(72*n+408)*x+72*x^2)*P(n-1,x) for n >= 1, with P(0,x) = 1012 + 816*x + 144*x^2.","mathematica":"P[0, x_] := 1012 + 816*x + 144*x^2;\nP[n_, x_] := P[n, x] = Expand[Together[((132*n + 506 + (72*n + 408)*x + 72*x^2)*P[n - 1, x])/(6*n + 17 + 6*x)]];\nTable[CoefficientList[P[n, x], x], {n, 0, 9}] // Flatten","pari":"P(N) = {my(v = vector(N + 1)); v[1] = 1012 + 816*x + 144*x^2; for(n = 1, N, my(i = n + 1); v[i] = ((132*n + 506 + (72*n + 408)*x + 72*x^2)*v[i - 1])/(6*n + 17 + 6*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-29d7c5a1e19b9d74","steps":["x \u21a6 x+1","D+1"],"edges":["e-e77df5b989acd52a","e-eb024cebc27862fa"],"text":"A038314 \u2192 x \u21a6 x+1 \u2192 D+1"},"headline":"A038314 \u2192 x \u21a6 x+1 \u2192 D+1","chain":null}