A368854 a(n) = n! * (n+1)! * (n+2)! * Sum_{k=0..n} (-1)^k/(k! * (k+1)! * (k+2)!).

1, 5, 121, 7259, 871081, 182927009, 61463475025, 30977591412599, 22303865817071281, 22080827158900568189, 29146691849748750009481, 50015723214168855016269395, 109234339499744779355532358681, 298209746834303247640603339199129

Offset: 0

Author

Seiichi Manyama, Jan 07 2024

Keywords

• nonn
• easy

Crossrefs

Cf. A000166, A368853.

Cf. A368839.

Programs

PARI

a(n) = n!*(n+1)!*(n+2)!*sum(k=0, n, (-1)^k/(k!*(k+1)!*(k+2)!));

Formula

a(n) = n * (n+1) * (n+2) * a(n-1) + (-1)^n.

a(n) ~ c * n!*(n+1)!*(n+2)!, where c = hypergeom([], [2, 3], -1)/2 = 0.42008149848198278018826635149001977031641229888902795699817... - Vaclav Kotesovec, Jan 08 2024