A307265 Expansion of Product_{k>=1} 1/(1 + (-x)^k/(1 - x)^k).

1, 1, 1, 2, 5, 12, 27, 58, 122, 257, 549, 1190, 2600, 5683, 12367, 26749, 57530, 123202, 263115, 561131, 1196248, 2550975, 5443115, 11620526, 24814735, 52979512, 113038103, 240936717, 512916683, 1090501249, 2315608462, 4911611864, 10408318627, 22040127864

Offset

0,4

Comments

First differences of the binomial transform of A000700.

Links

Table of n, a(n) for n=0..33.

Formula

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

a(n) ~ 2^(n-2) * exp(Pi*sqrt(n/3)/2 + Pi^2/96) / (3^(1/4) * n^(3/4)). - Vaclav Kotesovec, Apr 01 2019

Maple

a:=series(mul(1/(1+(-x)^k/(1-x)^k), k=1..50), x=0, 34): seq(coeff(a, x, n), n=0..33); # Paolo P. Lava, Apr 02 2019

Mathematica

nmax = 33; CoefficientList[Series[Product[1/(1 + (-x)^k/(1 - x)^k), {k, 1, nmax}], {x, 0, nmax}], x]

Crossrefs

Cf. A000700, A129519, A218482, A307264.

Sequence in context: A000325 A076878 A129983 * A083378 A116712 A000102

Adjacent sequences: A307262 A307263 A307264 * A307266 A307267 A307268

Keyword

nonn

Author

Ilya Gutkovskiy, Apr 01 2019

Status

approved