|
|
A277452
|
|
a(n) = Sum_{k=0..n} binomial(n,k) * n^k * k!.
|
|
7
|
|
|
1, 2, 13, 226, 7889, 458026, 39684637, 4788052298, 766526598721, 157108817646514, 40104442275129101, 12472587843118746322, 4641978487740740993233, 2036813028164774540010266, 1040451608604560812273060189, 612098707457003526384666111226
(list;
graph;
refs;
listen;
history;
text;
internal format)
|
|
|
OFFSET
|
0,2
|
|
LINKS
|
|
|
FORMULA
|
a(n) = exp(1/n) * n^n * Gamma(n+1, 1/n).
a(n) ~ n^n * n!.
a(n) = floor(n^n*n!*exp(1/n)), n > 0. - Peter McNair, Dec 20 2021
|
|
MAPLE
|
a := n -> simplify(hypergeom([1, -n], [], -n)):
# second Maple program:
b:= proc(n, k) option remember;
1 + `if`(n>0, k*n*b(n-1, k), 0)
end:
a:= n-> b(n$2):
|
|
MATHEMATICA
|
Flatten[{1, Table[Sum[Binomial[n, k]*n^k*k!, {k, 0, n}], {n, 1, 20}]}]
|
|
PROG
|
(PARI) a(n) = sum(k=0, n, binomial(n, k) * n^k * k!); \\ Michel Marcus, Sep 18 2018
|
|
CROSSREFS
|
|
|
KEYWORD
|
nonn
|
|
AUTHOR
|
|
|
STATUS
|
approved
|
|
|
|