A284467 Expansion of Product_{k>=1} (1 + x^(2*k-1))^(2*k-1)/(1 + x^(2*k))^(2*k).

1, 1, -2, 1, 2, -2, 0, -5, 10, 1, -15, 10, -1, 18, -39, 4, 50, -24, -14, -69, 165, -70, -83, -20, 154, 161, -550, 313, 55, 410, -960, 102, 1074, -406, -506, -1344, 3581, -1791, -833, -1833, 4995, 205, -6993, 2982, 2461, 7649, -19791, 9495, 4986, 9581, -26745, 0

Offset

0,3

Links

Robert Israel, Table of n, a(n) for n = 0..2000

Formula

G.f.: exp(Sum_{k>=1} (-1)^(k+1)*x^k/(k*(1 + x^k)^2)). - Ilya Gutkovskiy, Jun 20 2018

Maple

N:= 100: # to get a(0)..a(N)
P:= mul((1+x^(2*k-1))^(2*k-1)/(1+x^(2*k))^(2*k), k=1..N/2):
S:= series(P, x, N+1):
seq(coeff(S, x, j), j=0..N); # Robert Israel, Apr 16 2017

Mathematica

nmax = 60; CoefficientList[Series[Product[(1 + x^(2*k-1))^(2*k-1)/(1 + x^(2*k))^(2*k), {k, 1, nmax}], {x, 0, nmax}], x] (* Vaclav Kotesovec, Apr 15 2017 *)

Crossrefs

Cf. A224364, A262736, A278710, A281683, A284474.

Sequence in context: A008441 A253183 A108804 * A200227 A316230 A127249

Adjacent sequences: A284464 A284465 A284466 * A284468 A284469 A284470

Keyword

sign

Author

Seiichi Manyama, Apr 15 2017

Status

approved