A381387 E.g.f. A(x) satisfies A(x) = 1/( 1 - sinh(x * A(x)) )^2.

1, 2, 14, 182, 3520, 91002, 2954400, 115638014, 5303063552, 278979672050, 16565016146176, 1095997724407302, 79966475806040064, 6379010456725968362, 552344502268240535552, 51595059327775839277646, 5171865567269556457308160, 553764742712510134123863522

Offset: 0

Author

Seiichi Manyama, Feb 22 2025

Keywords

• nonn

Crossrefs

Cf. A136630, A381386.

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 A381386.

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

E.g.f.: (1/x) * Series_Reversion( x*(1 - sinh(x))^2 ).