A385376 -id:A385376 - cp's OEIS frontend

A385468 Expansion of e.g.f. 1/(1 - 2 * arctanh(x))^(1/2).

1, 1, 3, 17, 129, 1269, 15147, 213765, 3475329, 64020585, 1317472563, 29960707545, 746086414785, 20192521440285, 590166330458715, 18525204423695565, 621571306435103745, 22199954036873457105, 840913892465144800995, 33672216851574639900705

Offset: 0

Seiichi Manyama, Jun 30 2025

Cf. A296676, A385469.

Cf. A001147, A111594, A385376.

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

E.g.f.: 1/(1 - log((1+x)/(1-x)))^(1/2).
a(n) = Sum_{k=0..n} A001147(k) * A111594(n,k).
a(n) ~ 2 * (exp(1) + 1)^(n - 1/2) * n^n / (exp(n - 1/2) * (exp(1) - 1)^(n + 1/2)). - Vaclav Kotesovec, Jun 30 2025

A385377 Expansion of e.g.f. 1/(1 - 3 * arcsin(x))^(1/3).

Original entry on oeis.org

1, 1, 4, 29, 296, 3929, 64096, 1241437, 27834496, 709117073, 20232018944, 639064971293, 22138797783040, 834595012185193, 34013250713804800, 1490126154034917917, 69836524615835156480, 3486395656135414573985, 184703404516197170544640, 10349751400296465164293405

Offset: 0

Seiichi Manyama, Jun 27 2025

nonn

Cf. A189780, A385376.

Cf. A007559, A385343, A385347.

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

a(n) = Sum_{k=0..n} A007559(k) * A385343(n,k).

a(n) ~ sqrt(2*Pi) * cos(1/3)^(1/3) * n^(n - 1/6) / (Gamma(1/3) * 3^(1/3) * exp(n) * sin(1/3)^(n + 1/3)). - Vaclav Kotesovec, Jun 27 2025

cp's OEIS Frontend

A385468 Expansion of e.g.f. 1/(1 - 2 * arctanh(x))^(1/2).

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