A367552 a(n) = Sum_{d|n} (d^2-1)^n.
0, 9, 512, 50706, 7962624, 1838528498, 587068342272, 248158343164707, 134217728134217728, 90438270904261473426, 74300837068800000000000, 73119374851006048408704228, 84922087747184192618514874368, 114943537906488487820754156670578
Offset: 1
Keywords
Programs
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Mathematica
a[n_]:= Sum[(-1)^(n-k)*Binomial[n,k]*DivisorSigma[2*k,n],{k,0,n}]; Array[a,14] (* Stefano Spezia, Nov 22 2023 *) -
PARI
a(n) = sumdiv(n, d, (d^2-1)^n);
Formula
a(n) = Sum_{k=0..n} (-1)^(n-k) * binomial(n,k) * sigma_{2*k}(n).