A381304 E.g.f. A(x) satisfies A(x) = 1/( 1 - sinh(x * A(x)^(1/2)) / A(x)^(1/2) ).

1, 1, 2, 7, 36, 241, 1984, 19461, 222080, 2892361, 42350976, 688911763, 12329035264, 240789209025, 5096898326528, 116247332597833, 2842225449025536, 74165478671163601, 2057366115038003200, 60461340544432547391, 1876511245926278365184, 61336532673286072390321

Offset: 0

Author

Seiichi Manyama, Feb 19 2025

Keywords

• nonn

Crossrefs

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!*binomial(n/2+k/2+1, k)/(n/2+k/2+1)*a136630(n, k));

Formula

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