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%I #10 Aug 28 2018 13:07:26
%S 1,1,8,35,115,429,1425,4803,15398,48940,151046,459000,1373219,4037721,
%T 11723911,33566828,94993571,265722551,735543433,2015558930,5471271099,
%U 14719853084,39266487114,103908002173,272855152096,711272144097,1841162650896,4734074846631
%N Expansion of Product_{k>=1} (1 + k*x^k)^(k^2).
%H Vaclav Kotesovec, <a href="/A285240/b285240.txt">Table of n, a(n) for n = 0..5000</a>
%t nmax = 40; CoefficientList[Series[Product[(1 + k*x^k)^(k^2), {k,1,nmax}], {x,0,nmax}], x]
%t nmax = 40; s = 1 + x; Do[s*=Sum[Binomial[k^2, j]*k^j*x^(j*k), {j, 0, Floor[nmax/k] + 1}]; s = Select[Expand[s], Exponent[#, x] <= nmax &];, {k, 2, nmax}]; CoefficientList[s, x]
%Y Cf. A022629, A027998, A266891, A285241, A285242.
%K nonn
%O 0,3
%A _Vaclav Kotesovec_, Apr 15 2017
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