A363660 a(n) = Sum_{d|n} binomial(d+n,n).

2, 9, 24, 90, 258, 1043, 3440, 13419, 48850, 187836, 705444, 2725099, 10400614, 40233015, 155133856, 601820876, 2333606238, 9079958260, 35345263820, 137876637843, 538259060526, 2104292500739, 8233430727624, 32248866496625, 126410606580284

Offset

1,1

Links

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

Formula

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

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

Mathematica

a[n_] := DivisorSum[n, Binomial[# + n, n] &]; Array[a, 25] (* Amiram Eldar, Jul 17 2023 *)

Prog

(PARI) a(n) = sumdiv(n, d, binomial(d+n, n));

Crossrefs

Cf. A007503, A116963, A363628.

Cf. A000984, A134758, A343548, A343549, A363661.

Sequence in context: A122006 A200086 A143561 * A027302 A213720 A353822

Adjacent sequences: A363657 A363658 A363659 * A363661 A363662 A363663

Keyword

nonn

Author

Seiichi Manyama, Jun 14 2023

Status

approved