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begins:\n  0:                1;\n  1:               16,                1;\n  2:              400,               52,                1;\n  3:            14400,             2948,              116,              1;\n  4:           705600,           203072,            12344,            216,             1;\n  5:         45158400,         17154432,          1437472,          38480,           360,           1;\n  6:       3657830400,       1760601600,        191088544,        6978592,         99320,         556,         1;\n  7:     365783040000,     216690624000,      29277351936,     1370470592,      26445312,      224420,       812,      1;\n  8:   44259747840000,   31569232896000,    5164563101184,   297889587968,    7320665792,    83896832,    459088,   1136,    1;\n  9: 6373403688960000, 5379460107264000, 1043823600728064, 72189720393984, 2171980030720, 31566850240, 232641344, 869184, 1536, 1;\n","recurrence_sentence":"The row polynomials satisfy P(n,x) = (n^2+6*n+9+x)*P(n-1,x) + 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1;\n   4:              400,               52,                1;\n   5:            14400,             2948,              116,              1;\n   6:           705600,           203072,            12344,            216,             1;\n   7:         45158400,         17154432,          1437472,          38480,           360,           1;\n   8:       3657830400,       1760601600,        191088544,        6978592,         99320,         556,         1;\n   9:     365783040000,     216690624000,      29277351936,     1370470592,      26445312,      224420,       812,      1;\n  10:   44259747840000,   31569232896000,    5164563101184,   297889587968,    7320665792,    83896832,    459088,   1136,    1;\n  11: 6373403688960000, 5379460107264000, 1043823600728064, 72189720393984, 2171980030720, 31566850240, 232641344, 869184, 1536, 1;\n","recurrence_sentence":"The row polynomials satisfy P(n,x) = (n^2+2*n+1+x)*P(n-1,x) + (2*n+3)*x*d/dx P(n-1,x) + x^2*d^2/dx^2 P(n-1,x) for n >= 3, with P(2,x) = 1.","mathematica":"P[2, x_] := 1;\nP[n_, x_] := P[n, x] = Expand[(n^2 + 2*n + 1 + x)*P[n - 1, x] + (2*n + 3)*x*D[P[n - 1, x], x] + x^2*D[P[n - 1, x], {x, 2}]];\nTable[PadRight[CoefficientList[P[n, x], x], n - 1], {n, 2, 11}] // Flatten","pari":"P(N) = {my(v = vector(N - 1)); v[1] = 1; for(n = 3, N, my(i = n - 1); v[i] = (n^2 + 2*n + 1 + x)*v[i - 1] + (2*n + 3)*x*deriv(v[i - 1], x) + x^2*deriv(deriv(v[i - 1], x), x)); v};\nrow(n, p) = {my(c = Vecrev(p)); c = concat(c, vector(n - 1 - #c)); c};\nT(N) = {my(v = P(N)); concat(vector(#v, i, row(i + 1, v[i])))};\nT(11)","reading":{"first_row":0,"offset":2,"reversed":false,"trim_zeros":"none","regular_triangle":true}}],"derivation":{"root":"n-ee73bfb592710e97","steps":[],"edges":[],"text":"A371081"},"headline":"A371081: Triangle read by rows, (2, 2)-Lah numbers.","chain":null}