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A355987
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a(n) = n! * Sum_{k=1..n} 1/floor(n/k)!.
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3
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1, 3, 13, 61, 421, 2641, 23521, 203281, 2071441, 22407841, 286403041, 3453468481, 51122111041, 759194916481, 12216117513601, 203300293996801, 3811792426041601, 69634723878720001, 1444704854104512001, 29725332567567436801, 658231789483184716801
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OFFSET
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1,2
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LINKS
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FORMULA
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E.g.f.: (1/(1-x)) * Sum_{k>0} (1 - x^k) * (exp(x^k) - 1).
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MATHEMATICA
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a[n_] := n! * Sum[1/Floor[n/k]!, {k, 1, n}]; Array[a, 21] (* Amiram Eldar, Jul 22 2022 *)
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PROG
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(PARI) a(n) = n!*sum(k=1, n, 1/(n\k)!);
(PARI) my(N=30, x='x+O('x^N)); Vec(serlaplace(sum(k=1, N, (1-x^k)*(exp(x^k)-1))/(1-x)))
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CROSSREFS
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KEYWORD
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nonn
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AUTHOR
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STATUS
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approved
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