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 A346545 E.g.f.: Product_{k>=1} 1 / (1 - x^k)^(exp(x)/k). 8
 1, 1, 5, 26, 175, 1384, 12933, 135050, 1582901, 20380208, 286577757, 4352682256, 71247772121, 1244923243966, 23166410620637, 456940648889070, 9521696033968393, 208851154175983608, 4812156417656806393, 116112764199821653284, 2928658457243240595901, 77042063713731887400418 (list; graph; refs; listen; history; text; internal format)
 OFFSET 0,3 COMMENTS Exponential transform of A002746. LINKS Table of n, a(n) for n=0..21. FORMULA E.g.f.: exp( exp(x) * Sum_{k>=1} d(k) * x^k / k ). a(0) = 1; a(n) = Sum_{k=1..n} binomial(n-1,k-1) * A002746(k) * a(n-k). MATHEMATICA nmax = 21; CoefficientList[Series[Product[1/(1 - x^k)^(Exp[x]/k), {k, 1, nmax}], {x, 0, nmax}], x] Range[0, nmax]! nmax = 21; CoefficientList[Series[Exp[Exp[x] Sum[DivisorSigma[0, k] x^k/k, {k, 1, nmax}]], {x, 0, nmax}], x] Range[0, nmax]! A002746[n_] := Sum[Binomial[n, k] DivisorSigma[0, k] (k - 1)!, {k, 1, n}]; a[0] = 1; a[n_] := a[n] = Sum[Binomial[n - 1, k - 1] A002746[k] a[n - k], {k, 1, n}]; Table[a[n], {n, 0, 21}] CROSSREFS Cf. A000005, A002746, A028342, A346546, A346547, A346548. Sequence in context: A355672 A356597 A094422 * A179513 A302896 A368176 Adjacent sequences: A346542 A346543 A346544 * A346546 A346547 A346548 KEYWORD nonn AUTHOR Ilya Gutkovskiy, Sep 16 2021 STATUS approved

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Last modified September 13 07:42 EDT 2024. Contains 375877 sequences. (Running on oeis4.)