OFFSET
0,5
FORMULA
a(n) = [x^n] 1/(1 - x - n*x^4).
a(n) = hypergeom([(1-n)/4, (2-n)/4, (3-n)/4, -n/4], [(1-n)/3, (2-n)/3, -n/3], -256*n/27). - Stefano Spezia, Jan 09 2024
a(n) ~ (1/4) * exp(n^(3/4)/4 + sqrt(n)/16 + 5*n^(1/4)/384) * n^(n/4) * (1 + 30643/(40960*n^(1/4)) + 3749229947/(10066329600*sqrt(n)) + 15892274778169/(137438953472000*n^(3/4))). - Vaclav Kotesovec, Jan 09 2024
MATHEMATICA
Table[HypergeometricPFQ[{1/4 - n/4, 1/2 - n/4, 3/4 - n/4, -n/4}, {1/3 - n/3, 2/3 - n/3, -n/3}, -256*n/27], {n, 0, 20}] (* Vaclav Kotesovec, Jan 09 2024 *)
PROG
(PARI) a(n) = sum(k=0, n\4, n^k*binomial(n-3*k, k));
CROSSREFS
KEYWORD
nonn,easy
AUTHOR
Seiichi Manyama, Jan 09 2024
STATUS
approved