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a(n) = Sum_{k=1..n-1} tau(k) * sigma_2(n-k).
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%I #14 Jul 26 2024 10:21:14

%S 0,1,7,22,54,105,188,307,459,690,937,1307,1680,2260,2740,3588,4221,

%T 5402,6163,7714,8694,10723,11758,14449,15574,18884,20320,24228,25626,

%U 30768,32038,37985,39826,46515,47898,56877,57754,67433,69450,80062,81103,95034,94941

%N a(n) = Sum_{k=1..n-1} tau(k) * sigma_2(n-k).

%C Convolution of tau with sigma_2.

%F G.f.: ( Sum_{k>=1} x^k/(1 - x^k) ) * ( Sum_{k>=1} k^2 * x^k/(1 - x^k) ).

%o (PARI) a(n) = sum(k=1, n-1, sigma(k, 0)*sigma(n-k, 2));

%o (PARI) my(N=50, x='x+O('x^N)); concat(0, Vec(sum(k=1, N, x^k/(1-x^k))*sum(k=1, N, k^2*x^k/(1-x^k))))

%Y Cf. A000005, A001157, A055507, A191831.

%K nonn,easy

%O 1,3

%A _Seiichi Manyama_, Jul 26 2024