OFFSET
0,3
FORMULA
a(n) = Sum_{k=0..floor(n/3)} (n-2*k)^n * binomial(n-2*k,k).
a(n) ~ c * (1-2*r)^(2*(1-r)*n) * n^n / ((1-3*r)^((1-3*r)*n) * r^(r*n)), where r = 0.06730326916452804898090832100482072129668759014637687455288... is the root of the equation (1-2*r) * log((1-3*r)^3 / (r*(1-2*r)^2)) = 2 and c = 0.77456580764856204420602709595934338976380573814558378938814706465915... - Vaclav Kotesovec, Feb 20 2023
PROG
(PARI) my(N=20, x='x+O('x^N)); Vec(sum(k=0, N, (k*x*(1+(k*x)^2))^k))
(PARI) a(n) = sum(k=0, n\3, (n-2*k)^n*binomial(n-2*k, k));
CROSSREFS
KEYWORD
nonn
AUTHOR
Seiichi Manyama, Feb 19 2023
STATUS
approved