A320343 Expansion of e.g.f. 1/sqrt(1 - 2*log(1 + x)).

1, 1, 2, 8, 42, 294, 2472, 24828, 286164, 3751428, 54864408, 887989200, 15731200680, 303068103480, 6304498706880, 140890167340560, 3365469544248720, 85585469309951760, 2308349518803845280, 65819488298810181120, 1978202007765686904480, 62505106242073569018720, 2071320752120227622985600

Offset

0,3

Links

Table of n, a(n) for n=0..22.

Formula

a(n) = Sum_{k=0..n} Stirling1(n,k)*A001147(k).

a(n) ~ n^n / ((exp(1/2) - 1)^(n + 1/2) * exp(n - 1/4)). - Vaclav Kotesovec, Jan 29 2019

a(0) = 1; a(n) = Sum_{k=1..n} (-1)^(k-1) * (2 - k/n) * (k-1)! * binomial(n,k) * a(n-k). - Seiichi Manyama, Sep 11 2023

Maple

seq(n!*coeff(series(1/sqrt(1-2*log(1+x)), x=0, 23), x, n), n=0..22); # Paolo P. Lava, Jan 29 2019

Mathematica

nmax = 22; CoefficientList[Series[1/Sqrt[1 - 2 Log[1 + x]], {x, 0, nmax}], x] Range[0, nmax]!
Table[Sum[StirlingS1[n, k] (2 k - 1)!!, {k, 0, n}], {n, 0, 22}]

Crossrefs

Cf. A001147, A006252, A048994, A088501, A305404, A346978.

Sequence in context: A225108 A052646 A352646 * A002856 A093461 A191994

Adjacent sequences: A320340 A320341 A320342 * A320344 A320345 A320346

Keyword

nonn

Author

Ilya Gutkovskiy, Jan 22 2019

Status

approved