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 A294504 Binomial transform of A156616. 4
 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 (list; graph; refs; listen; history; text; internal format)
 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

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Last modified July 15 23:38 EDT 2024. Contains 374343 sequences. (Running on oeis4.)