A306843 a(n) = Sum_{d|n} binomial(n,d)^3.

1, 9, 28, 281, 126, 11592, 344, 365465, 593434, 16095134, 1332, 921113624, 2198, 40424993884, 27175280778, 2137777203097, 4914, 121331143444050, 6860, 6310445825215406, 1572228697798262, 351047164202718608, 12168, 20174300460344963864, 149975199312626

Offset: 1

Author

Seiichi Manyama, Mar 12 2019

Keywords

• nonn

Links

• Seiichi Manyama, Table of n, a(n) for n = 1..1000

Crossrefs

Sum_{d|n} binomial(n,d)^b: A000005 (b=0), A056045 (b=1), A174462 (b=2), this sequence (b=3).

Cf. A000172, A001093, A001158.

Programs

Mathematica

a[n_] := DivisorSum[n, Binomial[n, #]^3 &]; Array[a, 25] (* Amiram Eldar, Jun 13 2021 *)

PARI

{a(n) = sumdiv(n, d, binomial(n, d)^3)}

Formula

If p is prime, a(p) = A001093(p).