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 A356009 a(n) = n! * Sum_{k=1..n} Sum_{d|k} 1/(d * (k/d)!). 7
 1, 4, 15, 73, 390, 2641, 19208, 164585, 1541746, 16158341, 181370552, 2283224065, 30160914446, 434715492485, 6655132252876, 109315669969217, 1879289179364690, 34719396682318021, 666070910669770400, 13590051478686198401, 289043813095242038422 (list; graph; refs; listen; history; text; internal format)
 OFFSET 1,2 LINKS FORMULA E.g.f.: (1/(1-x)) * Sum_{k>0} (exp(x^k) - 1)/k. E.g.f.: -(1/(1-x)) * Sum_{k>0} log(1-x^k)/k!. PROG (PARI) a(n) = n!*sum(k=1, n, sumdiv(k, d, 1/(d*(k/d)!))); (PARI) my(N=30, x='x+O('x^N)); Vec(serlaplace(sum(k=1, N, (exp(x^k)-1)/k)/(1-x))) (PARI) my(N=30, x='x+O('x^N)); Vec(serlaplace(-sum(k=1, N, log(1-x^k)/k!)/(1-x))) CROSSREFS Cf. A087906, A356004. Sequence in context: A171005 A303229 A340355 * A307996 A230741 A020082 Adjacent sequences: A356006 A356007 A356008 * A356010 A356011 A356012 KEYWORD nonn AUTHOR Seiichi Manyama, Jul 23 2022 STATUS approved

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Last modified November 27 10:37 EST 2022. Contains 358369 sequences. (Running on oeis4.)