A368838 a(n) = n! * (n+3)! * Sum_{k=0..n} 1/(k! * (k+3)!).

1, 5, 51, 919, 25733, 1029321, 55583335, 3890833451, 342393343689, 36978481118413, 4807202545393691, 740309191990628415, 133255654558313114701, 27717176148129127857809, 6596687923254732430158543, 1781105739278777756142806611, 541456144740748437867413209745

Offset: 0

Author

Seiichi Manyama, Jan 07 2024

Keywords

• nonn
• easy

Crossrefs

Cf. A099597, A006040, A228229, A368837.

Programs

PARI

a(n) = n!*(n+3)!*sum(k=0, n, 1/(k!*(k+3)!));

Formula

a(n) = n*(n+3)*a(n-1) + 1.

a(n) ~ BesselI(3,2) * n! * (n+3)!. - Vaclav Kotesovec, Jan 09 2024