The OEIS is supported by the many generous donors to the OEIS Foundation.

 Year-end appeal: Please make a donation to the OEIS Foundation to support ongoing development and maintenance of the OEIS. We are now in our 59th year, we have over 358,000 sequences, and we’ve crossed 10,300 citations (which often say “discovered thanks to the OEIS”). Other ways to Give
 Hints (Greetings from The On-Line Encyclopedia of Integer Sequences!)
 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

Lookup | Welcome | Wiki | Register | Music | Plot 2 | Demos | Index | Browse | More | WebCam
Contribute new seq. or comment | Format | Style Sheet | Transforms | Superseeker | Recents
The OEIS Community | Maintained by The OEIS Foundation Inc.

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