A346978 Expansion of e.g.f. 1 / sqrt(1 + 2 * log(1 - x)).

1, 1, 4, 26, 234, 2694, 37812, 626352, 11962164, 258787812, 6255195168, 167072685240, 4886611129320, 155335056242040, 5332298685827760, 196590247328769120, 7747254471910795920, 324986515253994589200, 14458392906960271354560, 679977065168639138610720

Offset

0,3

Links

Seiichi Manyama, Table of n, a(n) for n = 0..390

Formula

a(n) = Sum_{k=0..n} |Stirling1(n,k)| * (2*k-1)!!.

a(n) ~ n^n / (exp(n/2) * (exp(1/2) - 1)^(n + 1/2)). - Vaclav Kotesovec, Aug 09 2021

a(0) = 1; a(n) = Sum_{k=1..n} (2 - k/n) * (k-1)! * binomial(n,k) * a(n-k). - Seiichi Manyama, Sep 09 2023

Mathematica

nmax = 19; CoefficientList[Series[1/Sqrt[1 + 2 Log[1 - x]], {x, 0, nmax}], x] Range[0, nmax]!
Table[Sum[Abs[StirlingS1[n, k]] (2 k - 1)!!, {k, 0, n}], {n, 0, 19}]

Crossrefs

Cf. A001147, A007840, A088500, A305404, A320343.

Sequence in context: A066224 A227917 A136227 * A000310 A054360 A124824

Adjacent sequences: A346975 A346976 A346977 * A346979 A346980 A346981

Keyword

nonn

Author

Ilya Gutkovskiy, Aug 09 2021

Status

approved