A255835 G.f.: Product_{k>=1} (1+x^k)^(2*k-1).

1, 1, 3, 8, 15, 34, 67, 133, 255, 486, 901, 1649, 2984, 5312, 9373, 16342, 28221, 48283, 81928, 137858, 230278, 381919, 629156, 1029933, 1675856, 2711288, 4362575, 6983196, 11122327, 17630798, 27820283, 43706461, 68375137, 106534093, 165340844, 255643289

Offset

0,3

Links

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

Formula

a(n) ~ Zeta(3)^(1/6) * exp(-Pi^4 / (2592*Zeta(3)) - Pi^2 * n^(1/3) / (12*(3*Zeta(3))^(1/3)) + 3^(4/3)/2 * Zeta(3)^(1/3) * n^(2/3)) / (2^(1/6) * 3^(1/3) * sqrt(Pi) * n^(2/3)), where Zeta(3) = A002117.

G.f.: exp(Sum_{k>=1} (-1)^(k+1)*x^k*(1 + x^k)/(k*(1 - x^k)^2)). - Ilya Gutkovskiy, Jun 07 2018

Mathematica

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

Crossrefs

Cf. A026007, A219555, A052812, A253289, A255834.

Sequence in context: A277224 A090741 A376764 * A032234 A032255 A137475

Adjacent sequences: A255832 A255833 A255834 * A255836 A255837 A255838

Keyword

nonn

Author

Vaclav Kotesovec, Mar 07 2015

Status

approved