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A306039 Expansion of e.g.f. Product_{k>=1} 1/(1 - log(1 + x)^k/k!). 2
1, 1, 2, 3, 14, 0, 359, -1988, 28706, -312210, 4387572, -62769366, 1006242599, -17203315363, 318393704043, -6296931104285, 133039045075494, -2986262905171914, 71018001954178952, -1783064497977512206, 47133484019671647932, -1308274154275749372040, 38042727898691562357962 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,3

LINKS

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

N. J. A. Sloane, Transforms

Eric Weisstein's World of Mathematics, Stirling Transform

FORMULA

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

a(n) = Sum_{k=0..n} Stirling1(n,k)*A005651(k).

MAPLE

a:=series(mul(1/(1-log(1+x)^k/k!), k=1..100), x=0, 23): seq(n!*coeff(a, x, n), n=0..22); # Paolo P. Lava, Mar 26 2019

MATHEMATICA

nmax = 22; CoefficientList[Series[Product[1/(1 - Log[1 + x]^k/k!), {k, 1, nmax}], {x, 0, nmax}], x] Range[0, nmax]!

nmax = 22; CoefficientList[Series[Exp[Sum[Sum[Log[1 + x]^(j k)/(k (j!)^k), {j, 1, nmax}], {k, 1, nmax}]], {x, 0, nmax}], x] Range[0, nmax]!

Table[Sum[StirlingS1[n, k] Total[Apply[Multinomial, IntegerPartitions[k], {1}]], {k, 0, n}], {n, 0, 22}]

CROSSREFS

Cf. A005651, A140585, A306040.

Sequence in context: A093553 A253575 A027673 * A285933 A281754 A282119

Adjacent sequences:  A306036 A306037 A306038 * A306040 A306041 A306042

KEYWORD

sign

AUTHOR

Ilya Gutkovskiy, Jun 17 2018

STATUS

approved

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Last modified January 23 04:16 EST 2020. Contains 331168 sequences. (Running on oeis4.)