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A023882
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Expansion of g.f.: 1/Product_{n>0} (1 - n^n * x^n).
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14
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1, 1, 5, 32, 304, 3537, 52010, 895397, 18016416, 410889848, 10523505770, 298220329546, 9274349837081, 313761671751672, 11474635626789410, 450964042480390679, 18954785687060988578, 848386888530723146912
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OFFSET
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0,3
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LINKS
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FORMULA
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Log of g.f.: Sum_{k>=1} (sigma(k, k+1)/k) x^k, where sigma(k, q) is the sum of the q-th powers of the divisors of k.
a(n) ~ n^n * (1 + exp(-1)/n + (1/2*exp(-1)+5*exp(-2))/n^2). - Vaclav Kotesovec, Dec 19 2015
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MAPLE
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seq(coeff(series(1/mul(1-k^k*x^k, k=1..n), x, n+1), x, n), n = 0 .. 20); # Muniru A Asiru, Oct 31 2018
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MATHEMATICA
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nmax=20; CoefficientList[Series[Product[1/(1-k^k*x^k), {k, 1, nmax}], {x, 0, nmax}], x] (* Vaclav Kotesovec, Dec 19 2015 *)
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PROG
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(PARI) m=20; x='x+O('x^m); Vec(prod(k=1, m, 1/(1-k^k*x^k))) \\ G. C. Greubel, Oct 30 2018
(Magma) m:=20; R<x>:=PowerSeriesRing(Rationals(), m); Coefficients(R! ( (&*[1/(1-k^k*x^k): k in [1..m]]) )); // G. C. Greubel, Oct 30 2018
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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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