A255836 G.f.: Product_{k>=1} (1+x^k)^(3*k+1).

1, 4, 13, 42, 117, 310, 785, 1896, 4433, 10062, 22248, 48080, 101821, 211682, 432795, 871520, 1730491, 3391894, 6568996, 12580316, 23841774, 44742634, 83193865, 153347110, 280336704, 508499474, 915540681, 1636805438, 2906642396, 5128530946, 8993376689

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 / (3888*Zeta(3)) + Pi^2 * n^(1/3) / (6^(5/3) * Zeta(3)^(1/3)) + 3^(5/3)/2^(4/3) * Zeta(3)^(1/3) * n^(2/3)) / (2^(17/12) * 3^(1/6) * sqrt(Pi) * n^(2/3)), where Zeta(3) = A002117.

Mathematica

nmax=50; CoefficientList[Series[Product[(1+x^k)^(3*k+1), {k, 1, nmax}], {x, 0, nmax}], x]

Crossrefs

Cf. A026007, A219555, A052812, A255271, A255834, A255835, A255837.

Sequence in context: A186202 A036366 A303863 * A109454 A357063 A307261

Adjacent sequences: A255833 A255834 A255835 * A255837 A255838 A255839

Keyword

nonn

Author

Vaclav Kotesovec, Mar 07 2015

Status

approved