A385468 -id:A385468 - cp's OEIS frontend

A385469 Expansion of e.g.f. 1/(1 - 3 * arctanh(x))^(1/3).

1, 1, 4, 30, 312, 4224, 70176, 1384032, 31590912, 819254016, 23792039424, 764912590848, 26970073390080, 1034798724320256, 42921327875788800, 1913760046417508352, 91281373260924026880, 4637755280044146032640, 250054580636566927441920, 14259891701316651909120000

Offset: 0

Seiichi Manyama, Jun 30 2025

nonn

Cf. A296676, A385468.

Cf. A007559, A111594.

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

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

a(n) = Sum_{k=0..n} A007559(k) * A111594(n,k).

A385470 Expansion of e.g.f. 1/(1 - 2 * arctanh(x)).

Original entry on oeis.org

1, 2, 8, 52, 448, 4848, 62912, 952992, 16496640, 321282816, 6952332288, 165489858048, 4297340166144, 120890184308736, 3662409013420032, 118879239686541312, 4115985952586858496, 151415632063102648320, 5897814669785134006272, 242489327746828076974080

Offset: 0

Seiichi Manyama, Jun 30 2025

Cf. A296676, A385471.

Cf. A111594, A385468.

With[{nn=20},CoefficientList[Series[1/(1-2ArcTanh[x]),{x,0,nn}],x] Range[0,nn]!] (* Harvey P. Dale, Jul 04 2025 *)

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

E.g.f.: B(x)^2, where B(x) is the e.g.f. of A385468.
E.g.f.: 1/(1 - log((1+x)/(1-x))).
a(n) = Sum_{k=0..n} 2^k * k! * A111594(n,k).
a(n) ~ 2^(3/2) * sqrt(Pi) * (1 + exp(1))^(n-1) * n^(n + 1/2) / (exp(n-1) * (exp(1) - 1)^(n+1)). - Vaclav Kotesovec, Jun 30 2025

cp's OEIS Frontend

A385469 Expansion of e.g.f. 1/(1 - 3 * arctanh(x))^(1/3).

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