A307264 Expansion of (1/(1 - x)) * Product_{k>=1} 1/(1 + (-x)^k/(1 - x)^k).

1, 2, 3, 5, 10, 22, 49, 107, 229, 486, 1035, 2225, 4825, 10508, 22875, 49624, 107154, 230356, 493471, 1054602, 2250850, 4801825, 10244940, 21865466, 46680201, 99659713, 212697816, 453634533, 966551216, 2057052465, 4372660927, 9284272791, 19692591418

Offset

0,2

Comments

Binomial transform of A000700.

Links

Table of n, a(n) for n=0..32.

Formula

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

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

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

Maple

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

Mathematica

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

Crossrefs

Cf. A000700, A218481, A266232.

Sequence in context: A103595 A293842 A014844 * A329244 A173271 A326574

Adjacent sequences: A307261 A307262 A307263 * A307265 A307266 A307267

Keyword

nonn

Author

Ilya Gutkovskiy, Apr 01 2019

Status

approved