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begins:\n  0:           61,           192,            144;\n  1:          595,          2700,           3888,           1728;\n  2:         6145,         36480,          77760,          69120,           20736;\n  3:        65527,        481260,        1362240,        1831680,         1140480,          248832;\n  4:       712909,       6243264,       22064400,       39882240,        38257920,        17915904,         2985984;\n  5:      7863667,      79997484,      339193008,      771422400,      1005177600,       736791552,       271724544,        35831808;\n  6:     87615745,    1015472640,     5023823616,    13780924416,     22745318400,     22852730880,     13377208320,      4013162496,       429981696;\n  7:    983726695,   12796248780,    72366255360,   232524794880,    465072233472,    595390279680,    481579499520,    232190115840,     58047528960,     5159780352;\n  8:  11112210781,  160308442560,  1020163591440,  3758281390080,   8835828986880,  13765649006592,  14263030333440,   9571392552960,   3889184440320,   825564856320,    61917364224;\n  9: 126142119187, 1998734904012, 14136195150000, 58741025999040, 158768050129920, 291673577631744, 369185616543744, 318906674380800, 181553321410560, 63284706017280, 11578547109888, 743008370688;\n","recurrence_sentence":"The row polynomials satisfy (n+2)*P(n,x) = -(25*n+25+(120*n+120)*x+(144*n+144)*x^2)*P(n-2,x) + (14*n+21+(24*n+36)*x)*P(n-1,x) for n >= 2, with P(0,x) = 61 + 192*x + 144*x^2, P(1,x) = 595 + 2700*x + 3888*x^2 + 1728*x^3.","mathematica":"P[0, x_] := 61 + 192*x + 144*x^2;\nP[1, x_] := 595 + 2700*x + 3888*x^2 + 1728*x^3;\nP[n_, x_] := P[n, x] = Expand[Together[(-(25*n + 25 + (120*n + 120)*x + (144*n + 144)*x^2)*P[n - 2, x] + (14*n + 21 + (24*n + 36)*x)*P[n - 1, x])/(n + 2)]];\nTable[CoefficientList[P[n, x], x], {n, 0, 9}] // Flatten","pari":"P(N) = {my(v = vector(N + 1)); v[1] = 61 + 192*x + 144*x^2; v[2] = 595 + 2700*x + 3888*x^2 + 1728*x^3; for(n = 2, N, my(i = n + 1); v[i] = (-(25*n + 25 + (120*n + 120)*x + (144*n + 144)*x^2)*v[i - 2] + (14*n + 21 + (24*n + 36)*x)*v[i - 1])/(n + 2)); 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-b31aa1a3fd93d174","steps":["basis A013609","basis A013610"],"edges":["e-060b1f8a928003b3","e-1f35af42ff238408"],"text":"A133214 \u2192 basis A013609 \u2192 basis A013610"},"headline":"A133214 \u2192 basis A013609 \u2192 basis A013610","chain":null}