A385469 -id:A385469 - 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

A385471 Expansion of e.g.f. 1/(1 - 3 * arctanh(x)).

Original entry on oeis.org

1, 3, 18, 168, 2088, 32472, 605952, 13192848, 328268160, 9189103104, 285808290048, 9778434400512, 364965976571904, 14756982055363584, 642580290860378112, 29979230177385750528, 1491908801018949697536, 78884742832151951278080, 4416389166601900315901952

Offset: 0

Seiichi Manyama, Jun 30 2025

Cf. A296676, A385470.

Cf. A111594, A385469.

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

E.g.f.: B(x)^3, where B(x) is the e.g.f. of A385469.
E.g.f.: 1/(1 - (3/2) * log((1+x)/(1-x))).
a(n) = Sum_{k=0..n} 3^k * k! * A111594(n,k).

cp's OEIS Frontend

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

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