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A318143
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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.
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0
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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
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OFFSET
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0,8
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LINKS
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EXAMPLE
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[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;
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MAPLE
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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);
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CROSSREFS
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Alternating row sums are 1.
Polynomials evaluated at x = 0 are 1.
T(n, n-1) = A051049(n-1) for n >= 1.
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KEYWORD
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AUTHOR
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STATUS
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approved
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