A381411 E.g.f. A(x) satisfies A(x) = exp( sinh(x * A(x)^2) / A(x)^2 ).

1, 1, 1, 2, 21, 252, 2645, 29248, 420777, 7789008, 160214281, 3480537568, 82299294077, 2172147323712, 63112534885725, 1969853583132672, 65473850077772881, 2323179959573426432, 88007266294215935121, 3540245668453458467328, 150353926528453088942821

Offset: 0

Author

Seiichi Manyama, Feb 23 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, (2*n-2*k+1)^(k-1)*a136630(n, k));

Formula

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