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A022595 Expansion of Product_{m >=1} (1+q^m)^31.

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%I A022595 #14 Sep 08 2022 08:44:46
%S A022595 1,31,496,5487,47337,340039,2118385,11763911,59384158,276491170,
%T A022595 1200703594,4906332242,18998567031,70120824201,247873586247,
%U A022595 842625902072,2764160465375,8776228494225,27038961793349,81019542614568,236575764828149,674366427736330,1879524499776454
%N A022595 Expansion of Product_{m >=1} (1+q^m)^31.
%H A022595 G. C. Greubel, <a href="/A022595/b022595.txt">Table of n, a(n) for n = 0..1000</a>
%F A022595 a(n) ~ (31/3)^(1/4) * exp(Pi * sqrt(31*n/3)) / (131072 * n^(3/4)). - _Vaclav Kotesovec_, Mar 05 2015
%t A022595 nmax=50; CoefficientList[Series[Product[(1+q^m)^31,{m,1,nmax}],{q,0,nmax}],q] (* _Vaclav Kotesovec_, Mar 05 2015 *)
%o A022595 (PARI) m=50; q='q+O('q^m); Vec(prod(n=1,m,(1+q^n)^31)) \\ _G. C. Greubel_, Mar 20 2018
%o A022595 (Magma) Coefficients(&*[(1+x^m)^31:m in [1..40]])[1..40] where x is PolynomialRing(Integers()).1; // _G. C. Greubel_, Mar 20 2018
%Y A022595 Column k=31 of A286335.
%K A022595 nonn
%O A022595 0,2
%A A022595 _N. J. A. Sloane_
%E A022595 Terms a(19) onward added by _G. C. Greubel_, Mar 20 2018