A385441 E.g.f. A(x) satisfies A(x) = exp( arcsinh(x * A(x)^3) ).

1, 1, 7, 99, 2145, 62985, 2340135, 105306075, 5568833025, 338526428625, 23261601738375, 1783052341945875, 150846228128621025, 13961656447904590425, 1403387191229030382375, 152244874971071908900875, 17729607712540283209274625, 2206069759660369525039742625, 292095560880436494680262138375

Offset: 0

Author

Seiichi Manyama, Jun 29 2025

Keywords

• nonn

Crossrefs

Cf. A001147, A385369, A385440, A385442.

Cf. A385343.

Programs

PARI

a(n) = 2^n*n!*binomial((4*n+1)/2, n)/(4*n+1);

Formula

E.g.f. A(x) satisfies A(x) = (1 + 2*x*A(x)^4)^(1/2).

a(n) = 2^n * n! * binomial((4*n+1)/2,n)/(4*n+1).

a(n) = Sum_{k=0..n} (3*n+1)^(k-1) * i^(n-k) * A385343(n,k), where i is the imaginary unit.

a(n) ~ 2^(3*n-1) * n^(n-1) / exp(n). - Vaclav Kotesovec, Jul 04 2025