A385421 Expansion of e.g.f. 1/(1 - arcsin(2*x))^(1/2).

1, 1, 3, 19, 153, 1689, 21867, 343995, 6114993, 124933425, 2820098643, 70897706595, 1939085791305, 57898697121225, 1859540697970875, 64312039377723915, 2371651908598754145, 93246340110716523105, 3882169166979871734435, 171024539858087082582195

Offset: 0

Author

Seiichi Manyama, Jun 28 2025

Keywords

• nonn

Crossrefs

Cf. A189780, A385422.

Cf. A001147, A001586, A385343.

Programs

PARI

my(N=20, x='x+O('x^N)); Vec(serlaplace(1/(1-asin(2*x))^(1/2)))

Formula

a(n) = Sum_{k=0..n} A001147(k) * 2^(n-k) * A385343(n,k).

a(n) ~ sqrt(sin(2)) * 2^n * n^n / (exp(n) * sin(1)^(n+1)). - Vaclav Kotesovec, Jun 28 2025