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A303483 a(n) = [x^n] Product_{k=1..n} ((1 + x^k)/(1 - x^k))^(n-k+1).

%I A303483 #6 May 04 2018 08:59:02
%S A303483 1,2,10,64,436,3072,22096,161148,1187118,8812050,65806720,493827256,
%T A303483 3720698056,28128081912,213258301824,1620878656280,12346263051028,
%U A303483 94221026620572,720267101230410,5514346833878672,42274910234115352,324490877248800232,2493471670778297856,19179885230907692452
%N A303483 a(n) = [x^n] Product_{k=1..n} ((1 + x^k)/(1 - x^k))^(n-k+1).
%F A303483 a(n) ~ c * d^n / sqrt(n), where d = 7.862983395705905261519347909953827161057584... and c = 0.23317816342157644853479309078... - _Vaclav Kotesovec_, May 04 2018
%e A303483 a(0) = 1;
%e A303483 a(1) = [x^1] (1 + x)/(1 - x) = 2;
%e A303483 a(2) = [x^2] ((1 + x)^2*(1 + x^2))/((1 - x)^2*(1 - x^2)) = 10;
%e A303483 a(3) = [x^3] ((1 + x)^3*(1 + x^2)^2*(1 + x^3))/((1 - x)^3*(1 - x^2)^2*(1 - x^3)) = 64;
%e A303483 a(4) = [x^4] ((1 + x)^4*(1 + x^2)^3*(1 + x^3)^2*(1 + x^4))/((1 - x)^4*(1 - x^2)^3*(1 - x^3)^2*(1 - x^4)) = 436;
%e A303483 a(5) = [x^5] ((1 + x)^5*(1 + x^2)^4*(1 + x^3)^3*(1 + x^4)^2*(1 + x^5))/((1 - x)^5*(1 - x^2)^4*(1 - x^3)^3*(1 - x^4)^2*(1 - x^5)) = 3072, etc.
%e A303483 ...
%e A303483 The table of coefficients of x^k in expansion of Product_{k=1..n} ((1 + x^k)/(1 - x^k))^(n-k+1) begins:
%e A303483 n = 0: (1),  0,   0,    0,    0,     0,  ...
%e A303483 n = 1:  1,  (2),  2,    2,    2,     2,  ...
%e A303483 n = 2:  1,   4, (10),  20,   34,    52,  ...
%e A303483 n = 3:  1,   6,  22,  (64), 158,   346,  ...
%e A303483 n = 4:  1,   8,  38,  140, (436), 1200,  ...
%e A303483 n = 5:  1,  10,  58,  256,  946, (3072), ...
%t A303483 Table[SeriesCoefficient[Product[((1 + x^k)/(1 - x^k))^(n - k + 1), {k, 1, n}], {x, 0, n}], {n, 0, 23}]
%Y A303483 Cf. A206228, A206229, A270919, A303173, A303174.
%K A303483 nonn
%O A303483 0,2
%A A303483 _Ilya Gutkovskiy_, Apr 24 2018