A241247 - OEIS

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

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OFFSET

1,1

LINKS

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

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))).

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}]

PROG

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