A308570 - OEIS

%I #19 Jun 09 2019 05:23:36

%S 1,17,730,65793,9765626,2177317874,678223072850,281479271743489,

%T 150094635684419611,100000095367432689202,81402749386839761113322,

%U 79496851942053939878082786,91733330193268616658399616010,123476696151234472370970011268514

%N a(n) = sigma_{2*n}(n).

%H Seiichi Manyama, <a href="/A308570/b308570.txt">Table of n, a(n) for n = 1..214</a>

%F L.g.f.: -log(Product_{k>=1} (1 - (k^2*x)^k)^(1/k)) = Sum_{k>=1} a(k)*x^k/k.

%F a(n) ~ n^(2*n). - _Vaclav Kotesovec_, Jun 08 2019

%t Table[DivisorSigma[2 n, n], {n, 1, 20}] (* _Vaclav Kotesovec_, Jun 08 2019 *)

%o (PARI) {a(n) = sigma(n, 2*n)}

%o (PARI) N=20; x='x+O('x^N); Vec(x*deriv(-log(prod(k=1, N, (1-(k^2*x)^k)^(1/k)))))

%Y Diagonal of A308504.

%Y Column k=2 of A308569.

%Y Cf. A073705.

%K nonn

%O 1,2

%A _Seiichi Manyama_, Jun 08 2019