OFFSET
0,5
LINKS
Winston de Greef, Table of n, a(n) for n = 0..1429
FORMULA
a(n) = n! * Sum_{k=0..floor(n/4)} 1/(k!^4 * (n-4*k)!).
G.f.: Sum_{k>=0} (4*k)!/k!^4 * x^(4*k)/(1-x)^(4*k+1).
From Vaclav Kotesovec, Mar 20 2023: (Start)
Recurrence: n^3*a(n) = (2*n - 1)*(2*n^2 - 2*n + 1)*a(n-1) - (n-1)*(6*n^2 - 12*n + 7)*a(n-2) + 2*(n-2)*(n-1)*(2*n - 3)*a(n-3) + 255*(n-3)*(n-2)*(n-1)*a(n-4).
a(n) ~ 5^(n + 3/2) / (2^(5/2) * Pi^(3/2) * n^(3/2)). (End)
PROG
(PARI) a(n) = n!*sum(k=0, n\4, 1/(k!^4*(n-4*k)!));
CROSSREFS
KEYWORD
nonn
AUTHOR
Seiichi Manyama, Mar 19 2023
STATUS
approved