A381210 Expansion of e.g.f. 1/(1 - sinh(x))^3.

1, 3, 12, 63, 408, 3123, 27552, 275103, 3065088, 37682883, 506606592, 7392091743, 116329479168, 1963781841843, 35395627487232, 678401549017983, 13776623985819648, 295481239628640003, 6674320861079273472, 158364407589097613823, 3937958237874411798528

Offset: 0

Author

Seiichi Manyama, Feb 17 2025

Keywords

• nonn

Crossrefs

Cf. A377530, A381207, A381209, A381211.

Cf. A136630.

Programs

PARI

a136630(n, k) = 1/(2^k*k!)*sum(j=0, k, (-1)^(k-j)*(2*j-k)^n*binomial(k, j));
a(n) = sum(k=0, n, (k+2)!*a136630(n, k))/2;

Formula

a(n) = 1/2 * Sum_{k=0..n} (k+2)! * A136630(n,k).