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a(n) = Sum_{d|n} (d^2+1)^n.
1

%I #11 Nov 22 2023 10:48:33

%S 2,29,1008,84162,11881408,2566742098,781250000128,318651789038947,

%T 167619551409708544,110462353708225871026,89116503268220597579776,

%U 86380568889558343409300388,99045780329059370000000008192

%N a(n) = Sum_{d|n} (d^2+1)^n.

%F a(n) = Sum_{k=0..n} binomial(n,k) * sigma_{2*k}(n).

%o (PARI) a(n) = sumdiv(n, d, (d^2+1)^n);

%Y Cf. A163190, A308570, A367552.

%K nonn

%O 1,1

%A _Seiichi Manyama_, Nov 22 2023