OFFSET
0,8
LINKS
Seiichi Manyama, Table of n, a(n) for n = 0..1000
FORMULA
a(n) = Sum_{k=0..n} binomial(k,n-3*k) * k^(n-3*k).
log(a(n)) ~ n/4 * log(n/4).
a(n) ~ exp(exp(1/4)*n^(1/4)/4^(1/4)) * n^(n/4) / 4^(n/4 + 1) * (1 + 1/(2^(5/2)*exp(1/4)*n^(1/4)) + (67/(192*exp(1/2)) - 15*exp(1/2)/16)/sqrt(n)).
MATHEMATICA
nmax = 50; CoefficientList[Series[Sum[(1 + k*x)^k * x^(3*k), {k, 0, nmax}], {x, 0, nmax}], x]
Join[{1}, Table[Sum[Binomial[k, n - 3*k] * k^(n - 3*k), {k, 0, n}], {n, 1, 50}]]
CROSSREFS
KEYWORD
nonn
AUTHOR
Vaclav Kotesovec, Feb 17 2023
STATUS
approved