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604800,  5454540, 36088416, 180972792,  700539840, 2111001750,  4953817440,  8984423448,  12380449536,  12573894060,   8928208800,   4017693960,    918330048,    43046721;\n  9: 55, 2808, 67473, 1013472, 10657980, 83280960, 500726772, 2366368992, 8899983378, 26795648880, 64596653550, 124025574816, 187447743756, 218562551424, 190266506820, 117087081120, 46103038191, 9298091736, 387420489;\n","recurrence_sentence":"The row polynomials satisfy (6*n-5+3*x)*P(n,x) = (6*n+1+(36*n+9)*x+(54*n+27)*x^2+27*x^3)*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[((6*n + 1 + (36*n + 9)*x + (54*n + 27)*x^2 + 27*x^3)*P[n - 1, x])/(6*n - 5 + 3*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] = ((6*n + 1 + (36*n + 9)*x + (54*n + 27)*x^2 + 27*x^3)*v[i - 1])/(6*n - 5 + 3*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-cdb0db4ad473ee28","steps":["basis A013610","D+1"],"edges":["e-4aebfd11077ddb65","e-0d1c0bf122d52e8c"],"text":"basis-map coefficients of A297191, shifted \u2192 basis A013610 \u2192 D+1"},"headline":"basis-map coefficients of A297191, shifted \u2192 basis A013610 \u2192 D+1","chain":null}