A285289 Expansion of Product_{k>=1} ((1 + x^k) / (1 + x^(2*k)))^k.

1, 1, 1, 4, 5, 10, 16, 26, 44, 68, 110, 167, 265, 399, 609, 919, 1371, 2040, 3005, 4420, 6436, 9364, 13501, 19433, 27806, 39639, 56265, 79572, 112126, 157390, 220283, 307163, 427145, 592029, 818359, 1127878, 1550483, 2125656, 2907013, 3965853, 5397497

Offset

0,4

Links

Vaclav Kotesovec, Table of n, a(n) for n = 0..1000

Formula

a(n) ~ exp(3^(5/3) * Zeta(3)^(1/3) * n^(2/3) / 4) * Zeta(3)^(1/6) / (2 * 3^(1/6) * sqrt(Pi) * n^(2/3)).

Mathematica

nmax = 50; CoefficientList[Series[Product[((1+x^k)/(1+x^(2*k)))^k, {k, 1, nmax}], {x, 0, nmax}], x]

Crossrefs

Cf. A263345, A285290, A285291.

Sequence in context: A002970 A073611 A058594 * A022309 A049897 A049867

Adjacent sequences: A285286 A285287 A285288 * A285290 A285291 A285292

Keyword

nonn

Author

Vaclav Kotesovec, Apr 16 2017

Status

approved