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A352843
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Expansion of e.g.f. exp(Sum_{k>=1} sigma_k(k) * x^k/k!).
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1
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1, 1, 6, 44, 491, 6597, 110652, 2144606, 47988524, 1206275925, 33777572464, 1040200674416, 34967153135940, 1273241146218823, 49928549099500206, 2097300313258417056, 93953420539864844743, 4470694981375022862697, 225184078001798318202935
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OFFSET
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0,3
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COMMENTS
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LINKS
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FORMULA
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a(0) = 1; a(n) = Sum_{k=1..n} sigma_k(k) * binomial(n-1,k-1) * a(n-k).
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MATHEMATICA
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nmax = 20; CoefficientList[Series[E^(Sum[DivisorSigma[k, k]*x^k/k!, {k, 1, nmax}]), {x, 0, nmax}], x] * Range[0, nmax]! (* Vaclav Kotesovec, Apr 15 2022 *)
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PROG
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(PARI) my(N=20, x='x+O('x^N)); Vec(serlaplace(exp(sum(k=1, N, sigma(k, k)*x^k/k!))))
(PARI) a(n) = if(n==0, 1, sum(k=1, n, sigma(k, k)*binomial(n-1, k-1)*a(n-k)));
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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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