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

Author

Peter Luschny, Aug 19 2018

Keywords

• nonn
• tabl

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

Row sums are (-1)^n*A009179(n).

Alternating row sums are 1.

Polynomials evaluated at x = 0 are 1.

T(n, n-1) = A051049(n-1) for n >= 1.

T(n, 1) = A000295(n) for n >= 0.

Cf. A046802, A173018.

Programs

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);