A373708 Expansion of e.g.f. exp(x * (1 + x^4)^2).
1, 1, 1, 1, 1, 241, 1441, 5041, 13441, 393121, 10946881, 99902881, 559025281, 2335441681, 182348406241, 4382526067921, 48882114328321, 355837396998721, 5157802930734721, 312898934463543361, 7129755898022511361, 89524038506304371761, 773103613914955683361
Offset: 0
Keywords
Programs
-
PARI
a(n) = n!*sum(k=0, 2*n\9, binomial(2*n-8*k, k)/(n-4*k)!);
Formula
a(n) = n! * Sum_{k=0..floor(2*n/9)} binomial(2*n-8*k,k)/(n-4*k)!.
a(n) == 1 (mod 240).
a(n) = a(n-1) + 10*(n-1)*(n-2)*(n-3)*(n-4)*a(n-5) + 9*(n-1)*(n-2)*(n-3)*(n-4)*(n-5)*(n-6)*(n-7)*(n-8)*a(n-9).