A241247 a(n) = Sum_{k=0..n} n^k * binomial(n,k)^3.

2, 21, 352, 8065, 231876, 7951069, 314931968, 14095941633, 701590424500, 38358147922501, 2281458125531520, 146469277526152321, 10084388675810865248, 740560093656498673965, 57738578482070455269376, 4760258648137662340202497, 413561386818608994516491316

Offset: 1

Author

Vaclav Kotesovec, Apr 18 2014

Keywords

• nonn
• easy

Links

• Vincenzo Librandi, Table of n, a(n) for n = 1..200

Crossrefs

Cf. A187021, A234971.

Programs

Mathematica

Table[Sum[n^k*Binomial[n,k]^3,{k,0,n}],{n,1,20}]
Table[HypergeometricPFQ[{-n,-n,-n},{1,1},-n],{n,1,20}]

PARI

a(n) = sum(k=0, n, n^k*binomial(n,k)^3); \\ Michel Marcus, Jul 11 2020

Formula

a(n) ~ exp(1 - 3*n^(1/3)/2 + 3*n^(2/3)) * n^(n-2/3) / (2*Pi*sqrt(3)) * (1 + 5/(4*n^(1/3))).