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

1,2

Links

Table of n, a(n) for n=1..14.

Formula

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

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 *)

Prog

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

Crossrefs

Cf. A163191, A367551.

Sequence in context: A112910 A180585 A102909 * A230671 A281443 A367446

Adjacent sequences: A367549 A367550 A367551 * A367553 A367554 A367555

Keyword

nonn

Author

Seiichi Manyama, Nov 22 2023

Status

approved