A385422 -id:A385422 - cp's OEIS frontend

A385420 Expansion of e.g.f. 1/(1 - arcsinh(3*x))^(1/3).

1, 1, 4, 19, 136, 1849, 28576, 383347, 6054016, 162756433, 4512553984, 94198960723, 2151597168640, 94600222614793, 3958651982848000, 103976698299157747, 2765446240371834880, 197818347558313860385, 11750108763413970288640, 335351034570439348695955

Offset: 0

Seiichi Manyama, Jun 28 2025

sign

a(28) = -1984619795429736510626124031150165852160.

Cf. A296675, A385419.

Cf. A007559, A385372, A385343, A385422.

my(N=20, x='x+O('x^N)); Vec(serlaplace(1/(1-asinh(3*x))^(1/3)))

E.g.f.: 1/(1 - log(3*x + sqrt(9*x^2 + 1)))^(1/3).

a(n) = Sum_{k=0..n} A007559(k) * (3*i)^(n-k) * A385343(n,k), where i is the imaginary unit.

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

Original entry on oeis.org

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

Offset: 0

Seiichi Manyama, Jun 28 2025

nonn

Cf. A189780, A385422.

Cf. A001147, A001586, A385343.

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

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

cp's OEIS Frontend

A385420 Expansion of e.g.f. 1/(1 - arcsinh(3*x))^(1/3).

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