OFFSET
0,2
FORMULA
a(n) = n! * Sum_{k=0..n} A341033(k,n)/k! = n! * (1 + Sum_{j=1.. n} Sum_{k=1.. j} n^(j-k) * binomial(j-1,k-1)/k!).
a(n) ~ BesselI(1,2) * n! * n^(n-1). - Vaclav Kotesovec, Feb 14 2021
EXAMPLE
a(3) = 3! * (1 + 1/1! + 7/2! + 73/3!) = 106.
MATHEMATICA
Table[n!*(1 + Sum[Sum[n^(j-k)*Binomial[j-1, k-1]/k!, {k, 1, j}], {j, 1, n}]), {n, 0, 20}] (* Vaclav Kotesovec, Feb 14 2021 *)
PROG
(PARI) {a(n) = n!*(1+sum(j=1, n, sum(k=1, j, n^(j-k)*binomial(j-1, k-1)/k!)))}
CROSSREFS
KEYWORD
nonn
AUTHOR
Seiichi Manyama, Feb 04 2021
STATUS
approved