A294502 Binomial transform of A026007.

1, 2, 5, 15, 45, 132, 381, 1086, 3060, 8531, 23563, 64560, 175639, 474790, 1275929, 3410180, 9068075, 23998671, 63230680, 165904474, 433596795, 1129037237, 2929620046, 7576584801, 19532878559, 50205938903, 128676829149, 328895341731, 838453003422

Offset

0,2

Links

Vaclav Kotesovec, Table of n, a(n) for n = 0..2960

Formula

a(n) = Sum_{k=0..n} binomial(n,k) * A026007(k).

a(n) ~ exp(3^(4/3) * Zeta(3)^(1/3) * n^(2/3) / 4 + (3*Zeta(3))^(2/3) * n^(1/3) / 8 - Zeta(3)/16) * Zeta(3)^(1/6) * 2^(n - 1/12) / (3^(1/3) * sqrt(Pi) * n^(2/3)).

G.f.: (1/(1 - x))*Product_{k>=1} (1 + x^k/(1 - x)^k)^k. - Ilya Gutkovskiy, Aug 19 2018

Mathematica

nmax = 40; s = CoefficientList[Series[Product[(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. A026007, A218481, A294500, A294503, A294504.

Sequence in context: A148353 A336417 A232208 * A254534 A071727 A148354

Adjacent sequences: A294499 A294500 A294501 * A294503 A294504 A294505

Keyword

nonn

Author

Vaclav Kotesovec, Nov 01 2017

Status

approved