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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. 0
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 (list; table; graph; refs; listen; history; text; internal format)
OFFSET

0,8

LINKS

Table of n, a(n) for n=0..54.

EXAMPLE

[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;

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);

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.

Sequence in context: A066298 A108068 A283998 * A131124 A131125 A187149

Adjacent sequences:  A318140 A318141 A318142 * A318144 A318145 A318146

KEYWORD

nonn,tabl

AUTHOR

Peter Luschny, Aug 19 2018

STATUS

approved

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Last modified October 16 20:36 EDT 2021. Contains 348047 sequences. (Running on oeis4.)