OFFSET
0,6
LINKS
Vaclav Kotesovec, Table of n, a(n) for n = 0..1000
FORMULA
a(n) = Sum_{k=0..n} binomial(k,n-2*k) * k^(n-2*k).
log(a(n)) ~ n/3 * log(n/3).
a(n) ~ exp(exp(1/3)*n^(1/3)/3^(1/3)) * n^(n/3) / 3^(n/3 + 1) * (1 + (3^(1/3)/(8*exp(1/3)) - 4*exp(2/3)/3^(5/3)) / n^(1/3) + (67/(128*3^(1/3)*exp(2/3)) + 8*exp(4/3)/3^(10/3)) / n^(2/3)).
MATHEMATICA
nmax = 40; CoefficientList[Series[Sum[(1 + k*x)^k * x^(2*k), {k, 0, nmax}], {x, 0, nmax}], x]
Join[{1}, Table[Sum[Binomial[k, n - 2*k] * k^(n - 2*k), {k, 0, n}], {n, 1, 40}]]
CROSSREFS
KEYWORD
nonn
AUTHOR
Vaclav Kotesovec, Feb 16 2023
STATUS
approved