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-6;\n   5:      24,       240,        600,         360,          24;\n   6:    -120,     -1800,      -7800,      -10800,       -3720,         -120;\n   7:     720,     15120,     100800,      252000,      216720,        45360,          720;\n   8:   -5040,   -141120,   -1340640,    -5292000,    -8573040,     -4868640,      -640080,       -5040;\n   9:   40320,   1451520,   18627840,   106686720,   280264320,    313286400,    121968000,    10281600,      40320;\n  10: -362880, -16329600, -272160000, -2133734400, -8283461760, -15431472000, -12376022400, -3385670400, -185431680, -362880;\n","recurrence_sentence":"The row polynomials satisfy P(n,x) = -(n-1+(n^2-2*n+1)*x)*P(n-1,x) + (n-1)*x^2*d/dx P(n-1,x) for n >= 2, with P(1,x) = 1.","mathematica":"P[1, x_] := 1;\nP[n_, x_] := P[n, x] = Expand[-(n - 1 + (n^2 - 2*n + 1)*x)*P[n - 1, x] + (n - 1)*x^2*D[P[n - 1, x], x]];\nTable[CoefficientList[P[n, x], x], {n, 1, 10}] // Flatten","pari":"P(N) = {my(v = vector(N)); v[1] = 1; for(n = 2, N, my(i = n); v[i] = -(n - 1 + (n^2 - 2*n + 1)*x)*v[i - 1] + (n - 1)*x^2*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, v[i])))};\nT(10)","reading":{"first_row":1,"offset":1,"reversed":false,"trim_zeros":"none","regular_triangle":false}}],"derivation":{"root":"n-cf1765de6ac2bd4b","steps":["basis A008277","reverse"],"edges":["e-2b559797932c7395","e-db734dbc16bfa9de"],"text":"basis-map coefficients of A021012 \u2192 basis A008277 \u2192 reverse"},"headline":"basis-map coefficients of A021012 \u2192 basis A008277 \u2192 reverse","chain":null}