|
%I #19 Mar 10 2023 10:13:37
%S 1,1,3,6,12,21,43,70,127,215,364,591,989,1562,2515,3954,6194,9538,
%T 14754,22349,33926,50910,76102,112721,166747,244205,356984,518344,
%U 749924,1078711,1547668,2207418,3140135,4446572,6276657,8823776,12371487,17275879,24061878
%N G.f.: Product_{i>=1, j>=1, k>=1} (1 + x^(i*j*k)).
%H Vaclav Kotesovec, <a href="/A280473/b280473.txt">Table of n, a(n) for n = 0..10000</a>
%H Lida Ahmadi, Ricardo Gómez Aíza, and Mark Daniel Ward, <a href="https://arxiv.org/abs/2303.02240">A unified treatment of families of partition functions</a>, arXiv:2303.02240 [math.CO], 2023.
%F G.f.: Product_{k>=1} (1 + x^k)^tau_3(k), where tau_3() = A007425. - _Ilya Gutkovskiy_, May 22 2018
%t nmax = 50; CoefficientList[Series[Product[(1+x^(i*j*k)), {i, 1, nmax}, {j, 1, nmax/i}, {k, 1, nmax/i/j}], {x, 0, nmax}], x]
%t nmax = 50; A007425 = Table[Sum[DivisorSigma[0, d], {d, Divisors[n]}], {n, 1, nmax}]; s = 1 + x; Do[s *= Sum[Binomial[A007425[[k]], j]*x^(j*k), {j, 0, nmax/k}]; s = Expand[s]; s = Take[s, Min[nmax + 1, Exponent[s, x] + 1, Length[s]]];, {k, 2, nmax}]; Take[CoefficientList[s, x], nmax + 1] (* _Vaclav Kotesovec_, Aug 30 2018 *)
%Y Cf. A007425, A107742, A174465, A219560, A280486.
%K nonn
%O 0,3
%A _Vaclav Kotesovec_, Jan 04 2017
|
