OFFSET
0,2
LINKS
Seiichi Manyama, Table of n, a(n) for n = 0..30
Eric Weisstein's World of Mathematics, Binomial Sums
FORMULA
a(n) ~ 2^(n/2) * Pi^(n/2) * n^(n^2 + n/2) / exp(n^2 - 1/12). - Vaclav Kotesovec, Nov 25 2017
MATHEMATICA
Table[Sum[(n!/(n - k)!)^k, {k, 0, n}], {n, 0, 10}]
Table[Sum[(Gamma[n + 1]/Gamma[k + 1])^(n - k), {k, 0, n}], {n, 0, 10}]
Table[Sum[(Binomial[n, k] k!)^k, {k, 0, n}], {n, 0, 10}]
PROG
(PARI) a(n) = sum(k=0, n, (n!/(n - k)!)^k); \\ Michel Marcus, Nov 25 2017
CROSSREFS
KEYWORD
nonn
AUTHOR
Ilya Gutkovskiy, Nov 24 2017
STATUS
approved