A022582 - OEIS

%I #21 Sep 08 2022 08:44:46

%S 1,17,153,986,5134,22967,91528,332741,1121864,3550518,10644516,

%T 30446116,83554915,221028152,565733446,1405559677,3398860779,

%U 8018057345,18489507853,41750241112,92455892640,201066321781,429927351485,904832464581,1876192580514,3836193955660,7740691696577

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

%H Seiichi Manyama, <a href="/A022582/b022582.txt">Table of n, a(n) for n = 0..10000</a>

%F a(n) ~ (17/3)^(1/4) * exp(Pi * sqrt(17*n/3)) / (1024 * n^(3/4)). - _Vaclav Kotesovec_, Mar 05 2015

%F a(0) = 1, a(n) = (17/n)*Sum_{k=1..n} A000593(k)*a(n-k) for n > 0. - _Seiichi Manyama_, Apr 04 2017

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

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

%Y Column k=17 of A286335.

%K nonn

%O 0,2

%A _N. J. A. Sloane_

%E More terms added by _G. C. Greubel_, Feb 25 2018