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A298905 Expansion of e.g.f. Product_{k>=1} (1 + log(1 + x)^k). 2
1, 1, 1, 8, -8, 224, -712, 9120, -53496, 980088, -14394648, 264140832, -4113747024, 59028225840, -545558201424, -4191307074432, 450100910950272, -17302659472138752, 530508727766191104, -14790496500550616832, 408513443917280375808, -12274212131738107257600 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,4

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} (-1)^(k+1)*log(1 + x)^k/(k*(1 - log(1 + x)^k))).

a(n) = Sum_{k=0..n} Stirling1(n,k)*A000009(k)*k!.

MAPLE

b:= proc(n) option remember; `if`(n=0, 1, add(b(n-j)*add(

     `if`(d::odd, d, 0), d=numtheory[divisors](j)), j=1..n)/n)

    end:

a:= n-> add(Stirling1(n, j)*b(j)*j!, j=0..n):

seq(a(n), n=0..23);  # Alois P. Heinz, Jun 18 2018

MATHEMATICA

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

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

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

CROSSREFS

Cf. A000009, A088311, A305550, A306023, A306042, A320350.

Sequence in context: A090630 A182922 A135808 * A059196 A027504 A078247

Adjacent sequences:  A298902 A298903 A298904 * A298906 A298907 A298908

KEYWORD

sign

AUTHOR

Ilya Gutkovskiy, Jun 18 2018

STATUS

approved

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Last modified July 19 03:54 EDT 2019. Contains 325144 sequences. (Running on oeis4.)