A318143 Coefficients of the polynomials generated by the e.g.f. cosh(x*z)*(x-1)/(x-exp(z*(x-1))), triangle read by rows, T(n,k) for 0 <= k <= n.
1, 1, 0, 1, 1, 1, 1, 4, 4, 0, 1, 11, 17, 7, 1, 1, 26, 76, 66, 16, 0, 1, 57, 317, 467, 237, 31, 1, 1, 120, 1212, 2962, 2612, 806, 64, 0, 1, 247, 4321, 17215, 24145, 13519, 2641, 127, 1, 1, 502, 14644, 92554, 199192, 178486, 65884, 8434, 256, 0
Offset: 0
Examples
[n\k][0, 1, 2, 3, 4, 5, 6, 7, 8] [0] 1; [1] 1, 0; [2] 1, 1, 1; [3] 1, 4, 4, 0; [4] 1, 11, 17, 7, 1; [5] 1, 26, 76, 66, 16, 0; [6] 1, 57, 317, 467, 237, 31, 1; [7] 1, 120, 1212, 2962, 2612, 806, 64, 0; [8] 1, 247, 4321, 17215, 24145, 13519, 2641, 127, 1;
Crossrefs
Programs
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Maple
gf := cosh(x*z)*(x-1)/(x-exp(z*(x-1))): ser := series(gf, z, 12): p := n -> normal(n!*coeff(ser, z, n)): seq(seq(coeff(p(n),x,k), k=0..n), n=0..10);