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A356342
a(n) = Sum_{k=1..n} binomial(2*n, k) * sigma_2(k).
0
2, 34, 281, 2178, 12397, 79729, 398932, 2224354, 10959221, 56341309, 255685080, 1334248401, 5892916876, 28082515768, 127714609741, 604178948098, 2590365128017, 12284868071365, 52160408294826, 241445420212893, 1049251819301974, 4674022621994716, 19563451165603647
OFFSET
1,1
FORMULA
a(n) ~ zeta(3) * n^2 * 2^(2*n-1).
MATHEMATICA
Table[Sum[Binomial[2*n, k]*DivisorSigma[2, k], {k, 1, n}], {n, 1, 30}]
PROG
(PARI) a(n) = sum(k=1, n, binomial(2*n, k) * sigma(k, 2)); \\ Michel Marcus, Aug 05 2022
CROSSREFS
KEYWORD
nonn
AUTHOR
Vaclav Kotesovec, Aug 04 2022
STATUS
approved