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A294530
Binomial transform of A023871.
3
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
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
KEYWORD
nonn
AUTHOR
Vaclav Kotesovec, Nov 02 2017
STATUS
approved