A022665 - OEIS

%I #17 Sep 08 2022 08:44:46

%S 1,-5,0,25,0,-26,-145,0,265,265,993,-825,-2070,-3190,-2335,2739,7890,

%T 29570,21085,-5250,-73006,-71945,-191140,-176805,185045,295675,

%U 1204590,1067375,1353655,-910885,-3688009,-4645850,-9409195,-12021485,-4296815,19981183,28942560,76843230,70996895

%N Expansion of Product_{m>=1} (1 - m*q^m)^5.

%H G. C. Greubel, <a href="/A022665/b022665.txt">Table of n, a(n) for n = 0..1000</a>

%F G.f.: exp(-5*Sum_{j>=1} Sum_{k>=1} k^j*x^(j*k)/j). - _Ilya Gutkovskiy_, Feb 07 2018

%t With[{nmax=50}, CoefficientList[Series[Product[(1-k*q^k)^5, {k,1,nmax}], {q, 0, nmax}],q]] (* _G. C. Greubel_, Feb 23 2018 *)

%o (PARI) m=50; q='q+O('q^m); Vec(prod(n=1,m,(1-n*q^n)^5)) \\ _G. C. Greubel_, Feb 23 2018

%o (Magma) Coefficients(&*[(1-m*x^m)^5:m in [1..40]])[1..40] where x is PolynomialRing(Integers()).1; // _G. C. Greubel_, Feb 23 2018

%Y Column k=5 of A297323.

%K sign

%O 0,2

%A _N. J. A. Sloane_

%E Terms a(32) onward added by _G. C. Greubel_, Feb 23 2018