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A320343 Expansion of e.g.f. 1/sqrt(1 - 2*log(1 + x)). 0
1, 1, 2, 8, 42, 294, 2472, 24828, 286164, 3751428, 54864408, 887989200, 15731200680, 303068103480, 6304498706880, 140890167340560, 3365469544248720, 85585469309951760, 2308349518803845280, 65819488298810181120, 1978202007765686904480, 62505106242073569018720, 2071320752120227622985600 (list; graph; refs; listen; history; text; internal format)
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

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.

Sequence in context: A078592 A225108 A052646 * A002856 A093461 A191994

Adjacent sequences:  A320340 A320341 A320342 * A320344 A320345 A320346

KEYWORD

nonn

AUTHOR

Ilya Gutkovskiy, Jan 22 2019

STATUS

approved

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Last modified November 13 21:28 EST 2019. Contains 329106 sequences. (Running on oeis4.)