A294529 Binomial transform of A001156.

1, 2, 4, 8, 17, 38, 86, 192, 420, 905, 1939, 4163, 8987, 19494, 42368, 91990, 199127, 429345, 921982, 1972553, 4206909, 8949412, 19001874, 40293048, 85373962, 180826115, 382957231, 811027414, 1717497958, 3636335170, 7695599294, 16275268520, 34389570596

Offset

0,2

Links

Vaclav Kotesovec, Table of n, a(n) for n = 0..3000

Formula

a(n) = Sum_{k=0..n} binomial(n,k) * A001156(k).

a(n) ~ exp(3 * 2^(-5/3) * Pi^(1/3) * Zeta(3/2)^(2/3) * n^(1/3)) * Zeta(3/2)^(2/3) * 2^(n - 7/6) / (sqrt(3) * Pi^(7/6) * n^(7/6)).

G.f.: (1/(1 - x))*Product_{k>=1} 1/(1 - x^(k^2)/(1 - x)^(k^2)). - Ilya Gutkovskiy, Aug 20 2018

Mathematica

nmax = 40; s = CoefficientList[Series[Product[1/(1 - x^(k^2)), {k, 1, nmax}], {x, 0, nmax}], x]; Table[Sum[Binomial[n, k] * s[[k+1]], {k, 0, n}], {n, 0, nmax}]

Crossrefs

Cf. A001156, A218481, A266232, A294500, A294530.

Sequence in context: A348756 A348755 A084635 * A154222 A114199 A006196

Adjacent sequences: A294526 A294527 A294528 * A294530 A294531 A294532

Keyword

nonn

Author

Vaclav Kotesovec, Nov 02 2017

Status

approved