OFFSET
0,3
LINKS
Seiichi Manyama, Table of n, a(n) for n = 0..373
FORMULA
a(n) = Sum_{k=0..floor(n/2)} (n-k)^n * binomial(n-k,k).
a(n) ~ c * d^n * n^n, where d = (1-r)^(2-r) / (r^r * (1-2*r)^(1-2*r)) where r = 0.163662210494891118101893756356803907477984542... is the root of the equation (1-2*r)^2 = r*(1-r) * exp(1/(1-r)) and c = 0.78619174295244329885973980954744130517052330684023764340463604028671858569... - Vaclav Kotesovec, Feb 14 2023
MATHEMATICA
Flatten[{1, Table[Sum[Binomial[n-k, k] * (n-k)^n, {k, 0, n/2}], {n, 1, 20}]}] (* Vaclav Kotesovec, Feb 14 2023 *)
PROG
(PARI) my(N=20, x='x+O('x^N)); Vec(sum(k=0, N, (k*x*(1+k*x))^k))
(PARI) a(n) = sum(k=0, n\2, (n-k)^n*binomial(n-k, k));
CROSSREFS
KEYWORD
nonn
AUTHOR
Seiichi Manyama, Feb 14 2023
STATUS
approved