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%I #10 Mar 06 2018 17:50:27
%S 1,2,16,144,1376,15800,210816,3333372,61688448,1318588146,32004369200,
%T 869282342632,26099925704928,857736429098848,30605729417479104,
%U 1177841009504482200,48614265201514729984,2141639401723095243324,100282931820560447963568,4973060138191518242569120
%N a(n) = [x^n] Product_{k>=1} ((1 + n*x^k)/(1 - n*x^k))^k.
%F a(n) ~ 2 * n^n * (1 + 4/n + 14/n^2 + 44/n^3 + 124/n^4 + 328/n^5 + 824/n^6 + 1980/n^7 + 4590/n^8 + 10320/n^9 + 22584/n^10 + ...), for coefficients see A261451. - _Vaclav Kotesovec_, Mar 05 2018
%e The table of coefficients of x^k in expansion of Product_{k>=1} ((1 + n*x^k)/(1 - n*x^k))^k begins:
%e n = 0: (1), 0, 0, 0, 0, 0, ...
%e n = 1: 1, (2), 6, 16, 38, 88, ...
%e n = 2: 1, 4, (16), 60, 192, 596, ...
%e n = 3: 1, 6, 30, (144), 582, 2280, ...
%e n = 4: 1, 8, 48, 280, (1376), 6568, ...
%e n = 5: 1, 10, 70, 480, 2790, (15800), ...
%t Table[SeriesCoefficient[Product[((1 + n x^k)/(1 - n x^k))^k, {k, 1, n}], {x, 0, n}], {n, 0, 19}]
%Y Cf. A156616, A261563, A266942, A270919, A270924, A292419, A298985, A298987.
%K nonn
%O 0,2
%A _Ilya Gutkovskiy_, Mar 05 2018
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