OFFSET
0,3
FORMULA
a(n) ~ 2^(2*n - 1/2) * n^(2*n - 1) / (sqrt(1+c) * c^(n + 1/2) * (2+c)^(n-1) * exp(2*n)), where c = LambertW(2*exp(-2)) = 0.21771510575709011079475830443312...
MAPLE
A346181 := proc(n)
add(binomial(n, k)*k^n*(k+1)^(n-1), k=0..n) ;
end proc:
seq(A346181(n), n=0..30) ; # R. J. Mathar, Mar 02 2023
MATHEMATICA
Join[{1}, Table[Sum[Binomial[n, k] * k^n * (k+1)^(n-1), {k, 0, n}], {n, 1, 20}]]
PROG
(PARI) a(n) = sum(k=0, n, binomial(n, k) * k^n * (k+1)^(n-1)); \\ Michel Marcus, Jul 09 2021
CROSSREFS
KEYWORD
nonn
AUTHOR
Vaclav Kotesovec, Jul 09 2021
STATUS
approved