A381383 E.g.f. A(x) satisfies A(x) = 1/( 1 - sinh(x * A(x)) / A(x) )^2.

1, 2, 6, 26, 176, 1842, 25552, 417146, 7727232, 162203810, 3855123968, 102712106202, 3024863555584, 97316416451282, 3393616911181824, 127581806046438074, 5147059194652983296, 221843071154521998402, 10172731970828970557440, 494451746675777509028762

Offset: 0

Author

Seiichi Manyama, Feb 22 2025

Keywords

• nonn

Crossrefs

Cf. A136630, A381382.

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

Formula

E.g.f.: B(x)^2, where B(x) is the e.g.f. of A381382.

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