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 A345751 E.g.f.: Product_{k>=1} (1 - (exp(x) - 1)^k)^(1/k). 4
 1, -1, -2, -3, -3, 40, 477, 4375, 45154, 486817, 5002397, 54970652, 732601449, 10046371231, 113632306694, 1051655108629, 12585372336141, 202763995934160, -863641466773595, -247388278229558697, -10810815349601723990, -311011007642247422759 (list; graph; refs; listen; history; text; internal format)
 OFFSET 0,3 COMMENTS Stirling transform of A028343. 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} d(k) * (exp(x) - 1)^k / k ), where d(n) is the number of divisors of n. a(n) = Sum_{k=0..n} Stirling2(n,k) * A028343(k). MATHEMATICA max = 21; Range[0, max]! * CoefficientList[Series[Product[(1 - (Exp[x] - 1)^k)^(1/k), {k, 1, max}], {x, 0, max}], x] (* Amiram Eldar, Jun 26 2021 *) PROG (PARI) my(N=40, x='x+O('x^N)); Vec(serlaplace(prod(k=1, N, (1-(exp(x)-1)^k)^(1/k)))) (PARI) my(N=40, x='x+O('x^N)); Vec(serlaplace(exp(-sum(k=1, N, numdiv(k)*(exp(x)-1)^k/k)))) CROSSREFS Cf. A000005, A028343, A048993, A336100, A345750, A345751, A345752. Sequence in context: A100650 A096502 A101462 * A242786 A214219 A365223 Adjacent sequences: A345748 A345749 A345750 * A345752 A345753 A345754 KEYWORD sign AUTHOR Seiichi Manyama, Jun 26 2021 STATUS approved

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Last modified September 17 19:04 EDT 2024. Contains 375990 sequences. (Running on oeis4.)