A307264 - OEIS

%I #9 Apr 03 2019 09:04:27

%S 1,2,3,5,10,22,49,107,229,486,1035,2225,4825,10508,22875,49624,107154,

%T 230356,493471,1054602,2250850,4801825,10244940,21865466,46680201,

%U 99659713,212697816,453634533,966551216,2057052465,4372660927,9284272791,19692591418

%N Expansion of (1/(1 - x)) * Product_{k>=1} 1/(1 + (-x)^k/(1 - x)^k).

%C Binomial transform of A000700.

%F G.f.: (1/(1 - x)) * Product_{k>=1} (1 + x^(2*k-1)/(1 - x)^(2*k-1)).

%F a(n) = Sum_{k=0..n} binomial(n,k)*A000700(k).

%F a(n) ~ 2^(n-1) * exp(Pi*sqrt(n/3)/2 + Pi^2/96) / (3^(1/4) * n^(3/4)). - _Vaclav Kotesovec_, Apr 01 2019

%p a:=series((1/(1-x))*mul(1/(1+(-x)^k/(1-x)^k),k=1..100),x=0,33): seq(coeff(a,x,n),n=0..32); # _Paolo P. Lava_, Apr 03 2019

%t nmax = 32; CoefficientList[Series[1/(1 - x) Product[1/(1 + (-x)^k/(1 - x)^k), {k, 1, nmax}], {x, 0, nmax}], x]

%Y Cf. A000700, A218481, A266232.

%K nonn

%O 0,2

%A _Ilya Gutkovskiy_, Apr 01 2019