%I #16 Sep 08 2022 08:44:46

%S 1,25,325,2950,21100,126905,667850,3157725,13667175,54900675,

%T 206841715,736953800,2499500175,8113694575,25320834800,76253908740,

%U 222308896150,629146702350,1732518057650,4651937973250,12201443983695,31311905220800,78732034002275,194220161393825

%N Expansion of Product_{m>=1} (1 + q^m)^25.

%H G. C. Greubel, <a href="/A022589/b022589.txt">Table of n, a(n) for n = 0..1000</a>

%F a(n) ~ sqrt(5) * exp(5 * Pi * sqrt(n/3)) / (16384 * 3^(1/4) * n^(3/4)). - _Vaclav Kotesovec_, Mar 05 2015

%t nmax=50; CoefficientList[Series[Product[(1+q^m)^25,{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)^25)) \\ _G. C. Greubel_, Feb 25 2018

%o (Magma) Coefficients(&*[(1+x^m)^25:m in [1..40]])[1..40] where x is PolynomialRing(Integers()).1; // _G. C. Greubel_, Feb 25 2018

%Y Column k=25 of A286335.

%K nonn

%O 0,2

%A _N. J. A. Sloane_

%E Terms a(20) onward added by _G. C. Greubel_, Feb 25 2018