A255834 G.f.: Product_{k>=1} (1+x^k)^(2*k+1).

1, 3, 8, 23, 55, 129, 291, 627, 1317, 2697, 5398, 10589, 20421, 38743, 72452, 133724, 243792, 439496, 784070, 1385195, 2424971, 4209094, 7247141, 12383496, 21008559, 35398548, 59259781, 98595110, 163077878, 268221706, 438791204, 714142139, 1156552537

Offset

0,2

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^(7/6)* 3^(1/3) * sqrt(Pi) * n^(2/3)), where Zeta(3) = A002117.

Mathematica

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

Crossrefs

Cf. A026007, A120844, A219555, A255835, A255836.

Sequence in context: A340493 A296286 A068602 * A027212 A027236 A353169

Adjacent sequences: A255831 A255832 A255833 * A255835 A255836 A255837

Keyword

nonn

Author

Vaclav Kotesovec, Mar 07 2015

Status

approved