A255802 G.f.: Product_{k>=1} 1/(1-x^k)^(2*k+3).

1, 5, 22, 79, 259, 777, 2201, 5911, 15239, 37865, 91224, 213741, 488759, 1093173, 2396934, 5160756, 10928181, 22787949, 46848176, 95046026, 190466354, 377295743, 739319876, 1433974869, 2754597217, 5243308562, 9894376295, 18517966608, 34386781020, 63378252332

Offset

0,2

Links

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

Formula

a(n) ~ Zeta(3)^(13/18) * exp(1/6 - Pi^4/(96*Zeta(3)) + Pi^2 * n^(1/3) / (2^(5/3) * Zeta(3)^(1/3)) + 3 * (Zeta(3)/2)^(1/3) * n^(2/3)) / (A^2 * 2^(5/9) * 3^(1/2) * Pi^2 * n^(11/9)), where A = A074962 = 1.2824271291... is the Glaisher-Kinkelin constant and Zeta(3) = A002117 = 1.202056903... .

Maple

with(numtheory): etr:= proc(p) local b; b:=proc(n) option remember; local d, j; if n=0 then 1 else add(add(d*p(d), d=divisors(j)) *b(n-j), j=1..n)/n fi end end: a:=etr(n-> 2*n+3): seq(a(n), n=0..50); # after Alois P. Heinz

Mathematica

nmax=50; CoefficientList[Series[Product[1/(1-x^k)^(2*k+3), {k, 1, nmax}], {x, 0, nmax}], x]

Crossrefs

Cf. A120844, A253289.

Sequence in context: A058750 A058752 A234351 * A266358 A183925 A296583

Adjacent sequences: A255799 A255800 A255801 * A255803 A255804 A255805

Keyword

nonn

Author

Vaclav Kotesovec, Mar 07 2015

Status

approved