A022635 - OEIS

%I #12 Sep 08 2022 08:44:46

%S 1,7,35,154,588,2065,6790,21071,62447,177863,489279,1305402,3389603,

%T 8587999,21280436,51674728,123161500,288539664,665292642,1511359766,

%U 3386065697,7488093282,16357998447,35324428405,75453678433,159512035137,333918915120,692516812176,1423479123640

%N Expansion of Product_{m>=1} (1 + m*q^m)^7.

%H G. C. Greubel, <a href="/A022635/b022635.txt">Table of n, a(n) for n = 0..1000</a>

%F G.f.: exp(7*Sum_{j>=1} Sum_{k>=1} (-1)^(j+1)*k^j*x^(j*k)/j). - _Ilya Gutkovskiy_, Feb 08 2018

%t With[{nmax = 50}, CoefficientList[Series[Product[(1 + k*q^k)^7, {k, 1, nmax}], {q, 0, nmax}], q]] (* _G. C. Greubel_, Feb 17 2018 *)

%o (PARI) m=50; q='q+O('q^m); Vec(prod(n=1,m,(1+n*q^n)^7)) \\ _G. C. Greubel_, Feb 17 2018

%o (Magma) Coefficients(&*[(1+m*x^m)^7:m in [1..40]])[1..40] where x is PolynomialRing(Integers()).1; // _G. C. Greubel_, Feb 17 2018

%Y Column k=7 of A297321.

%K nonn

%O 0,2

%A _N. J. A. Sloane_