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%I #24 Sep 08 2022 08:44:48
%S 1,1,3,12,79,722,8675,128177,2248873,45644104,1051632553,27107038863,
%T 772751427746,24136897360750,819689757351091,30068876227952332,
%U 1184869328943005936,49914047187427191742
%N Number of partitions in expanding space.
%H Vaclav Kotesovec, <a href="/A023879/b023879.txt">Table of n, a(n) for n = 0..380</a>
%F G.f.: Product_{k>=1} (1 - x^k)^(-k^(k-1)).
%F G.f.: exp( Sum_{n>=1} A062796(n)/n*x^n ), where A062796(n) = Sum_{d|n} d^d. - _Paul D. Hanna_, Sep 05 2012
%F a(n) ~ n^(n-1). - _Vaclav Kotesovec_, Mar 14 2015
%p seq(coeff(series(mul((1-x^k)^(-k^(k-1)),k=1..n),x,n+1), x, n), n = 0 .. 20); # _Muniru A Asiru_, Oct 31 2018
%t nmax=20; CoefficientList[Series[Product[1/(1-x^k)^(k^(k-1)),{k,1,nmax}],{x,0,nmax}],x] (* _Vaclav Kotesovec_, Mar 14 2015 *)
%o (PARI) {a(n)=polcoeff(prod(k=1,n,(1-x^k+x*O(x^n))^(-k^(k-1))),n)}
%o (PARI) {a(n)=polcoeff(exp(sum(m=1,n+1,sumdiv(m, d, d^d)*x^m/m) +x*O(x^n)),n)} \\ _Paul D. Hanna_, Sep 05 2012
%o (Magma) m:=30; R<x>:=PowerSeriesRing(Rationals(), m); Coefficients(R! ( (&*[1/(1-x^k)^(k^(k-1)): k in [1..m]]) )); // _G. C. Greubel_, Oct 31 2018
%Y Cf. A062796.
%K nonn
%O 0,3
%A _Olivier Gérard_
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