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8419950,       336798;\n  7:   61875000,   1599069384,    6086912832,    7017822504,    3210807600,     646652160,     56582064,     1732104;\n  8:  502734375,  21089542617,  116599030119,  189329162022,  122910444657,   36668882250,   5267183922,   349018956,    8444007;\n  9: 3910156250, 264793735206, 2093556825360, 4667297224590, 4133834514810, 1714391745066, 359569586376, 38696069412, 2009673666, 39405366;\n","recurrence_sentence":"The row polynomials satisfy n*P(n,x) = (5*n+25+(3*n+15)*x)*P(n-1,x) + (3*n+15)*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[Together[((5*n + 25 + (3*n + 15)*x)*P[n - 1, x] + (3*n + 15)*x*D[P[n - 1, x], x])/(n)]];\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 + 25 + (3*n + 15)*x)*v[i - 1] + (3*n + 15)*x*deriv(v[i - 1], x))/(n)); 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-97228a88c81561dc","steps":["basis A013610","basis A008277"],"edges":["e-3fa86ece9d0bedd1","e-55c161ba3b0b12e3"],"text":"A178822 \u2192 basis A013610 \u2192 basis A008277"},"headline":"A178822 \u2192 basis A013610 \u2192 basis A008277","chain":null}