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%I #17 Aug 16 2023 08:12:30
%S 1,12,102,688,4029,21156,102246,461448,1967658,7990996,31110432,
%T 116685288,423366831,1490904528,5110173678,17088259888,55862240688,
%U 178836472032,561532752086,1731639278904,5250722230962
%N Expansion of 1/Product_{m>=1} (1 - m*q^m)^12.
%C This sequence is obtained from the generalized Euler transform in A266964 by taking f(n) = 12, g(n) = n. - _Seiichi Manyama_, Aug 16 2023
%H Seiichi Manyama, <a href="/A022736/b022736.txt">Table of n, a(n) for n = 0..5000</a>
%F a(0) = 1; a(n) = (12/n) * Sum_{k=1..n} A078308(k) * a(n-k). - _Seiichi Manyama_, Aug 16 2023
%t With[{nmax = 50}, CoefficientList[Series[Product[(1 - k*q^k)^-12, {k, 1, nmax}], {q, 0, nmax}], q]] (* _G. C. Greubel_, Jul 25 2018 *)
%o (PARI) m=50; q='q+O('q^m); Vec(prod(n=1,m,(1-n*q^n)^-12)) \\ _G. C. Greubel_, Jul 25 2018
%o (Magma) n:=50; R<x>:=PowerSeriesRing(Integers(), n); Coefficients(R!(&*[(1/(1-m*x^m))^12:m in [1..n]])); // _G. C. Greubel_, Jul 25 2018
%Y Column k=12 of A297328.
%Y Cf. A078308.
%K nonn
%O 0,2
%A _N. J. A. Sloane_
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