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A306042 Expansion of e.g.f. Product_{k>=1} 1/(1 - log(1 + x)^k). 6
1, 1, 3, 8, 50, 94, 2446, -9024, 297216, -3183264, 64191984, -1041792192, 22098943632, -478805234064, 11856288460272, -308662348027008, 8575865689645440, -248582819381690880, 7556655091130023680, -240521346554744194560, 8049494171497089265920, -283469026458500121634560 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,3

LINKS

Table of n, a(n) for n=0..21.

N. J. A. Sloane, Transforms

Eric Weisstein's World of Mathematics, Stirling Transform

FORMULA

E.g.f.: exp(Sum_{k>=1} sigma(k)*log(1 + x)^k/k).

a(n) = Sum_{k=0..n} Stirling1(n,k)*A000041(k)*k!.

MAPLE

a:=series(mul(1/(1-log(1+x)^k), k=1..100), x=0, 22): seq(n!*coeff(a, x, n), n=0..21); # Paolo P. Lava, Mar 26 2019

MATHEMATICA

nmax = 21; CoefficientList[Series[Product[1/(1 - Log[1 + x]^k), {k, 1, nmax}], {x, 0, nmax}], x] Range[0, nmax]!

nmax = 21; CoefficientList[Series[Exp[Sum[DivisorSigma[1, k] Log[1 + x]^k/k, {k, 1, nmax}]], {x, 0, nmax}], x] Range[0, nmax]!

Table[Sum[StirlingS1[n, k] PartitionsP[k] k!, {k, 0, n}], {n, 0, 21}]

CROSSREFS

Cf. A000041, A006252, A053529, A167137, A320349.

Sequence in context: A305217 A316797 A000862 * A194364 A005444 A222684

Adjacent sequences:  A306039 A306040 A306041 * A306043 A306044 A306045

KEYWORD

sign

AUTHOR

Ilya Gutkovskiy, Jun 17 2018

STATUS

approved

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Last modified January 20 08:07 EST 2020. Contains 331081 sequences. (Running on oeis4.)