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a(n) = Sum_{k=1..n} binomial(2*n, k) * sigma(k).
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%I #7 Aug 05 2022 06:11:05

%S 2,22,131,806,3607,20395,84254,422230,1842359,8616007,33843614,

%T 173724659,676938316,2983855666,12806013721,57981927158,223432922515,

%U 1040923729567,4004885305320,18277809794671,75668287229078,317458937099194,1215454524390767,5785782106653667

%N a(n) = Sum_{k=1..n} binomial(2*n, k) * sigma(k).

%F a(n) ~ Pi^2 * n * 4^(n-1) / 3.

%t Table[Sum[Binomial[2*n, k]*DivisorSigma[1, k], {k, 1, n}], {n, 1, 30}]

%o (PARI) a(n) = sum(k=1, n, binomial(2*n, k) * sigma(k)); \\ _Michel Marcus_, Aug 05 2022

%Y Cf. A000203, A024916, A185003, A351146.

%K nonn

%O 1,1

%A _Vaclav Kotesovec_, Aug 04 2022