A022663 - OEIS

%I #26 Sep 08 2022 08:44:46

%S 1,-3,-3,8,9,18,-35,-33,-66,-91,216,189,386,315,333,-1483,-2268,-2214,

%T -1883,-456,-801,23032,12186,22665,18622,-20328,-39549,-78834,-146838,

%U -249342,-146662,15678,564771,238159,1274913,1398063,1572593,1423266,-833778,-3484732,-5261736,-9671502

%N Expansion of Product_{m>=1} (1 - m*q^m)^3.

%C This sequence is obtained from the generalized Euler transform in A266964 by taking f(n) = -3, g(n) = n. - _Seiichi Manyama_, Dec 29 2017

%H Seiichi Manyama, <a href="/A022663/b022663.txt">Table of n, a(n) for n = 0..1000</a>

%F G.f.: exp(-3*Sum_{j>=1} Sum_{k>=1} k^j*x^(j*k)/j). - _Ilya Gutkovskiy_, Feb 07 2018

%t With[{nmax=34}, CoefficientList[Series[Product[(1-k*q^k)^3, {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)^3)) \\ _G. C. Greubel_, Feb 23 2018

%o (Magma) Coefficients(&*[(1-m*x^m)^3:m in [1..40]])[1..40] where x is PolynomialRing(Integers()).1; // _G. C. Greubel_, Feb 23 2018

%Y Column k=3 of A297323.

%K sign

%O 0,2

%A _N. J. A. Sloane_

%E More terms added by _G. C. Greubel_, Feb 23 2018