OFFSET
0,4
LINKS
Vaclav Kotesovec, Graph - the asymptotic ratio (10000 terms)
FORMULA
a(n) = Sum_{k=0..floor(n/3)} (n-2*k)^k * binomial(n-2*k,k).
a(n) ~ exp(exp(2/3)*n^(2/3)/3^(2/3) - 5*exp(4/3)*n^(1/3)/(18*3^(1/3)) + 22*exp(2)/81) * n^(n/3) / 3^(n/3 + 1) * (1 + (2*exp(2/3)/3^(5/3) - 3295*exp(8/3)/(2916*3^(2/3)))/n^(1/3) + (3^(2/3)/(8*exp(2/3)) + 35*exp(4/3)/(36*3^(1/3)) + 27379*exp(10/3)/(17496*3^(1/3)) + 10857025*exp(16/3)/(51018336*3^(1/3)))/n^(2/3)). - Vaclav Kotesovec, Feb 20 2023
MATHEMATICA
Join[{1}, Table[Sum[Binomial[n - 2*k, k] * (n - 2*k)^k, {k, 0, n/3}], {n, 1, 30}]] (* Vaclav Kotesovec, Feb 20 2023 *)
PROG
(PARI) my(N=40, x='x+O('x^N)); Vec(sum(k=0, N, (x*(1+k*x^2))^k))
(PARI) a(n) = sum(k=0, n\3, (n-2*k)^k*binomial(n-2*k, k));
CROSSREFS
KEYWORD
nonn
AUTHOR
Seiichi Manyama, Feb 19 2023
STATUS
approved