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

1, 31, 496, 5487, 47337, 340039, 2118385, 11763911, 59384158, 276491170, 1200703594, 4906332242, 18998567031, 70120824201, 247873586247, 842625902072, 2764160465375, 8776228494225, 27038961793349, 81019542614568, 236575764828149, 674366427736330, 1879524499776454

Offset: 0

Author

N. J. A. Sloane

Keywords

• nonn

Links

• G. C. Greubel, Table of n, a(n) for n = 0..1000

Crossrefs

Column k=31 of A286335.

Programs

Magma

Coefficients(&*[(1+x^m)^31:m in [1..40]])[1..40] where x is PolynomialRing(Integers()).1; // G. C. Greubel, Mar 20 2018

Mathematica

nmax=50; CoefficientList[Series[Product[(1+q^m)^31,{m,1,nmax}],{q,0,nmax}],q] (* Vaclav Kotesovec, Mar 05 2015 *)

PARI

m=50; q='q+O('q^m); Vec(prod(n=1,m,(1+q^n)^31)) \\ G. C. Greubel, Mar 20 2018

Formula

a(n) ~ (31/3)^(1/4) * exp(Pi * sqrt(31*n/3)) / (131072 * n^(3/4)). - Vaclav Kotesovec, Mar 05 2015

Extensions

Terms a(19) onward added by G. C. Greubel, Mar 20 2018