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A346039 Expansion of e.g.f. Product_{k>=1} exp(1 - exp(x^k))^(1/k!). 3
1, -1, -1, 3, 1, 17, -119, 165, 1191, -21989, 169527, -317837, -7182779, 54452161, 292654649, -4320853051, -46883217705, 728176373539, 9943868087879, -166076498591597, -2748733072385043, 65290726021558089, 151614363753006601, -11661992771499644571 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,4

LINKS

Seiichi Manyama, Table of n, a(n) for n = 0..464

FORMULA

E.g.f.: exp( Sum_{k>=1} (1 - exp(x^k))/k! ).

E.g.f.: exp( -Sum_{k>=1} A121860(k)*x^k/k! ).

a(n) = -(n-1)! * Sum_{k=1..n} k * (Sum_{d|k} 1/(d! * (k/d)!)) * a(n-k)/(n-k)! for n > 0.

PROG

(PARI) my(N=40, x='x+O('x^N)); Vec(serlaplace(prod(k=1, N, exp(1-exp(x^k))^(1/k!))))

(PARI) my(N=40, x='x+O('x^N)); Vec(serlaplace(exp(sum(k=1, N, (1-exp(x^k))/k!))))

(PARI) my(N=40, x='x+O('x^N)); Vec(serlaplace(exp(-sum(k=1, N, sumdiv(k, d, 1/(d!*(k/d)!))*x^k))))

(PARI) a(n) = if(n==0, 1, -(n-1)!*sum(k=1, n, k*sumdiv(k, d, 1/(d!*(k/d)!))*a(n-k)/(n-k)!));

CROSSREFS

Cf. A000587, A121860, A330199, A345762, A346037, A346058.

Sequence in context: A350078 A151918 A089974 * A143849 A335689 A105626

Adjacent sequences: A346036 A346037 A346038 * A346040 A346041 A346042

KEYWORD

sign

AUTHOR

Seiichi Manyama, Jul 02 2021

STATUS

approved

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Last modified November 29 18:13 EST 2022. Contains 358431 sequences. (Running on oeis4.)