|
|
A241247
|
|
a(n) = Sum_{k=0..n} n^k * binomial(n,k)^3.
|
|
9
|
|
|
2, 21, 352, 8065, 231876, 7951069, 314931968, 14095941633, 701590424500, 38358147922501, 2281458125531520, 146469277526152321, 10084388675810865248, 740560093656498673965, 57738578482070455269376, 4760258648137662340202497, 413561386818608994516491316
(list;
graph;
refs;
listen;
history;
text;
internal format)
|
|
|
OFFSET
|
1,1
|
|
LINKS
|
|
|
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
|
|
CROSSREFS
|
|
|
KEYWORD
|
nonn,easy
|
|
AUTHOR
|
|
|
STATUS
|
approved
|
|
|
|