A022582 Expansion of Product_{m>=1} (1+x^m)^17.

1, 17, 153, 986, 5134, 22967, 91528, 332741, 1121864, 3550518, 10644516, 30446116, 83554915, 221028152, 565733446, 1405559677, 3398860779, 8018057345, 18489507853, 41750241112, 92455892640, 201066321781, 429927351485, 904832464581, 1876192580514, 3836193955660, 7740691696577

Offset: 0

Author

N. J. A. Sloane

Keywords

• nonn

Links

• Seiichi Manyama, Table of n, a(n) for n = 0..10000

Crossrefs

Column k=17 of A286335.

Programs

Magma

Coefficients(&*[(1+x^m)^17:m in [1..40]])[1..40] where x is PolynomialRing(Integers()).1; // G. C. Greubel, Feb 25 2018

Mathematica

nmax=50; CoefficientList[Series[Product[(1+q^m)^17,{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)^17)) \\ G. C. Greubel, Feb 25 2018

Formula

a(n) ~ (17/3)^(1/4) * exp(Pi * sqrt(17*n/3)) / (1024 * n^(3/4)). - Vaclav Kotesovec, Mar 05 2015

a(0) = 1, a(n) = (17/n)*Sum_{k=1..n} A000593(k)*a(n-k) for n > 0. - Seiichi Manyama, Apr 04 2017

Extensions

More terms added by G. C. Greubel, Feb 25 2018