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%I #25 Sep 08 2022 08:46:15
%S 1,1,4,31,283,3489,50913,890635,17891170,409850236,10494427982,
%T 297780829216,9261266862273,313453533534739,11464487066049791,
%U 450644378868285130,18942868694407904729,847930346323808122469,40266107916200371331007,2021842180288047801103956
%N Expansion of Product_{k>=1} (1 + k^k*x^k).
%H Vaclav Kotesovec, <a href="/A265949/b265949.txt">Table of n, a(n) for n = 0..380</a>
%F a(n) ~ n^n * (1 + exp(-1)/n + ((1/2)*exp(-1) + 4*exp(-2))/n^2).
%F G.f.: exp(Sum_{k>=1} ( Sum_{d|k} (-1)^(k/d + 1)*d^(k+1) ) * x^k/k). - _Ilya Gutkovskiy_, Nov 08 2018
%p seq(coeff(series(mul((1+k^k*x^k),k=1..n),x,n+1), x, n), n = 0 .. 20); # _Muniru A Asiru_, Oct 31 2018
%t nmax=20; CoefficientList[Series[Product[(1+k^k*x^k), {k, 1, nmax}], {x, 0, nmax}], x]
%o (PARI) m=30; x='x+O('x^m); Vec(prod(k=1, m, (1+k^k*x^k))) \\ _G. C. Greubel_, Oct 31 2018
%o (Magma) m:=30; R<x>:=PowerSeriesRing(Rationals(), m); Coefficients(R! ( (&*[(1+k^k*x^k): k in [1..m]]) )); // _G. C. Greubel_, Oct 31 2018
%Y Cf. A023882, A292190, A292305, A292306.
%K nonn
%O 0,3
%A _Vaclav Kotesovec_, Dec 19 2015
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