A363667 a(n) = Sum_{d|n} (n/d)^(n-n/d) * binomial(d+n-2,n-1).

1, 3, 7, 37, 71, 751, 925, 13161, 45676, 262911, 184757, 18014557, 2704157, 133062875, 2838201061, 16907954129, 601080391, 830283170617, 9075135301, 87074953375981, 246003195539410, 53321730394923, 2104098963721, 479275771000215865, 1952680410445479976

Offset

1,2

Links

Table of n, a(n) for n=1..25.

Formula

a(n) = [x^n] Sum_{k>0} x^k/(1 - (k*x)^k)^n.

Mathematica

a[n_] := DivisorSum[n, (n/#)^(n-n/#) * Binomial[# + n - 2, n - 1] &]; Array[a, 25] (* Amiram Eldar, Jul 12 2023 *)

Prog

(PARI) a(n) = sumdiv(n, d, (n/d)^(n-n/d)*binomial(d+n-2, n-1));

Crossrefs

Cf. A342628, A359112, A363650.

Cf. A363664, A363666.

Sequence in context: A252795 A049493 A260380 * A260382 A260381 A260378

Adjacent sequences: A363664 A363665 A363666 * A363668 A363669 A363670

Keyword

nonn

Author

Seiichi Manyama, Jun 14 2023

Status

approved