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begins:\n  0:            1;\n  1:            5,              3;\n  2:           50,             78,              18;\n  3:          750,           2322,            1296,             162;\n  4:        15000,          83304,           84888,           24624,            1944;\n  5:       375000,        3557160,         5918400,         2997000,          534600,           29160;\n  6:     11250000,      177493680,       454643280,       358279200,       108475200,        13122000,         524880;\n  7:    393750000,    10175896080,     38734899840,     44658870480,     20432412000,      4115059200,      360067680,      11022480;\n  8:  15750000000,   660707349120,   3652892691840,   5931431089920,   3850620923520,   1148787360000,   165013873920,   10934300160,    264539520;\n  9: 708750000000, 47996179136640, 379475474918400, 845988420009600, 749293640726400, 310748489735040, 65175130621440, 7014000833280, 364270919040, 7142567040;\n","recurrence_sentence":"The row polynomials satisfy P(n,x) = (5*n+3*n*x)*P(n-1,x) + 3*n*x*d/dx P(n-1,x) for n >= 1, with P(0,x) = 1.","mathematica":"P[0, x_] := 1;\nP[n_, x_] := P[n, x] = Expand[(5*n + 3*n*x)*P[n - 1, x] + 3*n*x*D[P[n - 1, x], x]];\nTable[CoefficientList[P[n, x], x], {n, 0, 9}] // Flatten","pari":"P(N) = {my(v = vector(N + 1)); v[1] = 1; for(n = 1, N, my(i = n + 1); v[i] = (5*n + 3*n*x)*v[i - 1] + 3*n*x*deriv(v[i - 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-cb5d49e71e46f2ed","steps":["basis A013610","basis A008277"],"edges":["e-542183e09dec6678","e-9dffbccef179bea3"],"text":"A196347 \u2192 basis A013610 \u2192 basis A008277"},"headline":"A196347 \u2192 basis A013610 \u2192 basis A008277","chain":null}