A294530 Binomial transform of A023871.

1, 2, 8, 33, 131, 497, 1834, 6635, 23622, 82942, 287656, 986552, 3349165, 11263951, 37558235, 124240204, 407951848, 1330340478, 4310385956, 13881618570, 44451643311, 141578435571, 448634389388, 1414774796929, 4441038400458, 13879652908322, 43197263002063

Offset

0,2

Links

Vaclav Kotesovec, Table of n, a(n) for n = 0..2600

Formula

a(n) = Sum_{k=0..n} binomial(n,k) * A023871(k).

a(n) ~ exp(2^(5/4) * 3^(-5/4) * 5^(-1/4) * Pi * n^(3/4) + Pi^2 * sqrt(n) / (4*sqrt(30)) - Pi^3 * n^(1/4) / (32 * 2^(1/4) * 15^(3/4)) + Pi^4/3840 - Zeta(3)/(4*Pi^2)) * 2^(n - 7/8) / (15^(1/8) * n^(5/8)).

G.f.: (1/(1 - x))*exp(Sum_{k>=1} sigma_3(k)*x^k/(k*(1 - x)^k)). - Ilya Gutkovskiy, Aug 20 2018

Mathematica

nmax = 40; s = CoefficientList[Series[Product[1/(1 - x^k)^(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. A023871, A218481, A266232, A294500, A294529.

Sequence in context: A084039 A135620 A134708 * A037513 A037716 A373752

Adjacent sequences: A294527 A294528 A294529 * A294531 A294532 A294533

Keyword

nonn

Author

Vaclav Kotesovec, Nov 02 2017

Status

approved