A381430 E.g.f. A(x) satisfies A(x) = 1 + sinh(x*A(x)^3).

1, 1, 6, 73, 1368, 34861, 1126368, 44135701, 2034072960, 107823563641, 6463383851520, 432331180935457, 31924171503581184, 2579483385868484005, 226383845487041421312, 21445302563389991287981, 2180974075392495296544768, 237009522316557393020262001, 27409082977094100068471537664

Offset: 0

Author

Seiichi Manyama, Feb 23 2025

Keywords

• nonn

Links

• Index entries for reversions of series

Crossrefs

Cf. A162653, A198865.

Cf. A136630, A381443.

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(3*n+1, k)*a136630(n, k))/(3*n+1);

Formula

E.g.f.: ( (1/x) * Series_Reversion( x/(1 + sinh(x))^3 ) )^(1/3).

a(n) = (1/(3*n+1)) * Sum_{k=0..n} k! * binomial(3*n+1,k) * A136630(n,k).