A385419 Expansion of e.g.f. 1/(1 - arcsinh(2*x))^(1/2).

1, 1, 3, 11, 57, 489, 5067, 50595, 573297, 9323985, 168823443, 2679252795, 45149256105, 1121782132665, 29930127386715, 629179051311315, 13329925622622945, 472248682257228705, 17395967794618282275, 434384524558247177835, 10095605146704332967705

Offset: 0

Author

Seiichi Manyama, Jun 28 2025

Keywords

• sign

Comments

a(32) = -243211075187578815197768727974208613120575.

Crossrefs

Cf. A296675, A385420.

Cf. A001147, A385371, A385343.

Programs

PARI

my(N=30, x='x+O('x^N)); Vec(serlaplace(1/(1-asinh(2*x))^(1/2)))

Formula

E.g.f.: 1/(1 - log(2*x + sqrt(4*x^2 + 1)))^(1/2).

a(n) = Sum_{k=0..n} A001147(k) * (2*i)^(n-k) * A385343(n,k), where i is the imaginary unit.