A022668 - OEIS

%I #13 Sep 08 2022 08:44:46

%S 1,-8,12,48,-106,-128,8,880,1041,-2560,-2524,-6720,5030,30880,26696,

%T 9264,-136524,-152456,-172604,37824,938316,1568960,1225624,-1981904,

%U -4585531,-10791440,-8363184,2558560,29452194,67002976,59590976,77029104,-140261287,-367505912,-536229932

%N Expansion of Product_{m>=1} (1 - m*q^m)^8.

%H G. C. Greubel, <a href="/A022668/b022668.txt">Table of n, a(n) for n = 0..1000</a>

%F G.f.: exp(-8*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)^8, {k, 1, nmax}], {q, 0, nmax}], q]] (* _G. C. Greubel_, Feb 24 2018 *)

%o (PARI) m=50; q='q+O('q^m); Vec(prod(n=1,m,(1-n*q^n)^8)) \\ _G. C. Greubel_, Feb 24 2018

%o (Magma) Coefficients(&*[(1-m*x^m)^8:m in [1..40]])[1..40] where x is PolynomialRing(Integers()).1; // _G. C. Greubel_, Feb 24 2018

%Y Column k=8 of A297323.

%K sign

%O 0,2

%A _N. J. A. Sloane_

%E Terms a(30) onward added by _G. C. Greubel_, Feb 24 2018