OFFSET
0,3
FORMULA
a(n) = Sum_{k=0..n} binomial(n, k) * A059297(n, k).
log(a(n)) ~ n*(log(n) - log(log(n)) - 1 + (3*log(log(n)) + 2)/log(n) - 1/log(n)^2). - Vaclav Kotesovec, Nov 12 2023
MAPLE
a := n -> add(binomial(n, k)^2*k^(n - k), k = 0 .. n):
seq(a(n), n = 0..22);
MATHEMATICA
Join[{1}, Table[Sum[Binomial[n, k]^2 * k^(n-k), {k, 0, n}], {n, 1, 20}]] (* Vaclav Kotesovec, Nov 12 2023 *)
CROSSREFS
KEYWORD
nonn
AUTHOR
Peter Luschny, Nov 11 2023
STATUS
approved