|
%I #21 Sep 08 2022 08:44:46
%S 1,13,91,468,1989,7384,24739,76427,220948,604175,1575392,3941847,
%T 9511944,22226049,50458447,111609537,241099027,509680951,1056262792,
%U 2149214288,4299359012,8465605408,16424772637,31429372312,59365381608,110770031489,204315725953,372772306309,673125106316
%N Expansion of Product_{m>=1} (1+x^m)^13.
%H Seiichi Manyama, <a href="/A022578/b022578.txt">Table of n, a(n) for n = 0..10000</a>
%F a(n) ~ (13/3)^(1/4) * exp(Pi * sqrt(13*n/3)) / (256 * n^(3/4)). - _Vaclav Kotesovec_, Mar 05 2015
%F a(0) = 1, a(n) = (13/n)*Sum_{k=1..n} A000593(k)*a(n-k) for n > 0. - _Seiichi Manyama_, Apr 03 2017
%t nmax=50; CoefficientList[Series[Product[(1+q^m)^13,{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)^13)) \\ _G. C. Greubel_, Feb 25 2018
%o (Magma) Coefficients(&*[(1+x^m)^13:m in [1..40]])[1..40] where x is PolynomialRing(Integers()).1; // _G. C. Greubel_, Feb 25 2018
%Y Column k=13 of A286335.
%K nonn
%O 0,2
%A _N. J. A. Sloane_
%E More terms added by _G. C. Greubel_, Feb 25 2018
|
