A381303 E.g.f. A(x) satisfies A(x) = 1/( 1 - sinh(x * A(x)^(1/2)) / A(x)^(3/2) ).

1, 1, 0, 1, 4, 1, 32, 183, 192, 4921, 33664, 88573, 2100224, 16487745, 83890176, 1920800731, 17243373568, 143156073841, 3236025171968, 33490813489497, 401094916964352, 9092346624868321, 109434837281013760, 1724106500663768191, 39706910863092875264

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).