A293193 a(n) = n! * [x^n] exp(n*arctanh(x)).

1, 1, 4, 33, 384, 5745, 105120, 2273985, 56770560, 1606455585, 50810457600, 1776342038625, 68018227200000, 2831056111508625, 127263741276672000, 6144722994699914625, 317153340121153536000, 17425813179911850338625, 1015487574490836615168000, 62559446107077837491198625

Offset: 0

Author

Ilya Gutkovskiy, Oct 02 2017

Keywords

• nonn

Crossrefs

Cf. A000246.

Programs

Mathematica

Table[n! SeriesCoefficient[Exp[n ArcTanh[x]], {x, 0, n}], {n, 0, 19}]
Table[n! SeriesCoefficient[Exp[n Sum[x^(2 k + 1)/(2 k + 1), {k, 0, Infinity}]], {x, 0, n}], {n, 0, 19}]

Formula

a(n) ~ phi^(5*n/2) * n^n / (5^(1/4) * exp(n)), where phi = A001622 = (1+sqrt(5))/2 is the golden ratio. - Vaclav Kotesovec, Oct 02 2017