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%I #7 Jun 11 2015 06:26:18
%S 1,1,2,6,16,51,166,554,1896,6595,23212,82582,296393,1071738,3900696,
%T 14278074,52526972,194108087,720197524,2681854490,10019539112,
%U 37545876368,141080872362,531457445806,2006678785762,7593123695669,28789152013570,109356019134584
%N a(n) = [x^n] Product_{k=1..n} (1+x^k)^2 / x^k.
%F a(n) ~ sqrt(3) * 4^n / (sqrt(Pi) * n^(3/2)).
%t Table[SeriesCoefficient[Product[(1+x^k)^2/x^k, {k, 1, n}], {x, 0, n}], {n, 0, 30}]
%t Table[SeriesCoefficient[Product[1+x^k, {k, 1, n}]^2, {x, 0, n*(n+3)/2}], {n, 0, 30}]
%Y Cf. A258798, A258799.
%K nonn
%O 0,3
%A _Vaclav Kotesovec_, Jun 10 2015
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