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

%I #13 Nov 22 2023 10:48:28

%S 0,9,512,50706,7962624,1838528498,587068342272,248158343164707,

%T 134217728134217728,90438270904261473426,74300837068800000000000,

%U 73119374851006048408704228,84922087747184192618514874368,114943537906488487820754156670578

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

%F a(n) = Sum_{k=0..n} (-1)^(n-k) * binomial(n,k) * sigma_{2*k}(n).

%t a[n_]:= Sum[(-1)^(n-k)*Binomial[n,k]*DivisorSigma[2*k,n],{k,0,n}]; Array[a,14] (* _Stefano Spezia_, Nov 22 2023 *)

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

%Y Cf. A163191, A367551.

%K nonn

%O 1,2

%A _Seiichi Manyama_, Nov 22 2023