OFFSET
0,3
LINKS
Alois P. Heinz, Table of n, a(n) for n = 0..345
FORMULA
a(n) = Sum_{k=0..n} (n+k+1)^(k-1) * Stirling2(n,k).
a(n) ~ sqrt(s^3 * (1+s) / (1 + r^2*s^2*(1+s) + r*s*(3 + 2*s))) * n^(n-1) / (exp(n) * r^(n - 1/2)), where r = 0.1609673785833512641321517974482987852086944930869... and s = 1.597727491873940099115048788232158935283220293884... are real roots of the system of equations exp(r*s)*s = s + log(s), exp(r*s)*(1 + r*s) = 1 + 1/s. - Vaclav Kotesovec, Nov 22 2021
MATHEMATICA
a[n_] := Sum[(n + k + 1)^(k - 1) * StirlingS2[n, k], {k, 0, n}]; Array[a, 18, 0] (* Amiram Eldar, Nov 22 2021 *)
PROG
(PARI) a(n) = sum(k=0, n, (n+k+1)^(k-1)*stirling(n, k, 2));
CROSSREFS
KEYWORD
nonn
AUTHOR
Seiichi Manyama, Nov 21 2021
STATUS
approved