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%I #22 Sep 08 2022 08:44:46
%S 1,21,231,1792,11067,58002,268093,1120899,4315269,15497986,52441347,
%T 168487473,517184185,1524390777,4332440454,11914441196,31798680774,
%U 82574231187,209091601271,517272712845,1252351944165,2971700764941,6920411525727,15835150526244,35640093688017
%N Expansion of Product_{m>=1} (1+x^m)^21.
%H Seiichi Manyama, <a href="/A022586/b022586.txt">Table of n, a(n) for n = 0..10000</a>
%F a(n) ~ 7^(1/4) * exp(Pi * sqrt(7*n)) / (4096 * n^(3/4)). - _Vaclav Kotesovec_, Mar 05 2015
%F a(0) = 1, a(n) = (21/n)*Sum_{k=1..n} A000593(k)*a(n-k) for n > 0. - _Seiichi Manyama_, Apr 04 2017
%t nmax=50; CoefficientList[Series[Product[(1+q^m)^21,{m,1,nmax}],{q,0,nmax}],q] (* _Vaclav Kotesovec_, Mar 05 2015 *)
%o (PARI) m=50; q='q+O('q^m); Vec(prod(n=1,m,(1+q^n)^21)) \\ _G. C. Greubel_, Feb 25 2018
%o (Magma) Coefficients(&*[(1+x^m)^21:m in [1..40]])[1..40] where x is PolynomialRing(Integers()).1; // _G. C. Greubel_, Feb 25 2018
%Y Column k=21 of A286335.
%K nonn
%O 0,2
%A _N. J. A. Sloane_
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