A294504 Binomial transform of A156616.

1, 3, 11, 41, 147, 509, 1717, 5671, 18395, 58735, 184961, 575337, 1769981, 5390997, 16270587, 48696299, 144620059, 426428645, 1249007767, 3635595953, 10520770265, 30278391475, 86689798089, 246988386691, 700439171501, 1977660342139, 5560497703461

Offset

0,2

Links

Vaclav Kotesovec, Table of n, a(n) for n = 0..2840

Formula

a(n) = Sum_{k=0..n} binomial(n,k) * A156616(k).

a(n) ~ exp(3 * (7*Zeta(3))^(1/3) * n^(2/3) / 4 + (7*Zeta(3))^(2/3) * n^(1/3) / 8 + 1/12 - 7*Zeta(3)/48) * (7*Zeta(3))^(7/36) * 2^(n - 1/12) / (A * sqrt(3*Pi) * n^(25/36)), where A is the Glaisher-Kinkelin constant A074962.

G.f.: (1/(1 - x))*exp(Sum_{k>=1} (sigma_2(2*k) - sigma_2(k))*x^k/(2*k*(1 - x)^k)). - Ilya Gutkovskiy, Oct 15 2018

Mathematica

nmax = 40; s = CoefficientList[Series[Product[((1+x^k)/(1-x^k))^k, {k, 1, nmax}], {x, 0, nmax}], x]; Table[Sum[Binomial[n, k] * s[[k+1]], {k, 0, n}], {n, 0, nmax}]

Crossrefs

Cf. A156616, A218481, A294500, A294502, A294505.

Sequence in context: A181863 A075276 A242233 * A086972 A218348 A320827

Adjacent sequences: A294501 A294502 A294503 * A294505 A294506 A294507

Keyword

nonn

Author

Vaclav Kotesovec, Nov 01 2017

Status

approved