A368837 a(n) = n! * (n+2)! * Sum_{k=0..n} 1/(k! * (k+2)!).

1, 4, 33, 496, 11905, 416676, 20000449, 1260028288, 100802263041, 9979424041060, 1197530884927201, 171246916544589744, 28769481979491076993, 5610048986000760013636, 1256650972864170243054465, 320445998080363411978888576

Offset: 0

Author

Seiichi Manyama, Jan 07 2024

Keywords

• nonn
• easy

Crossrefs

Cf. A099597, A006040, A228229, A368838.

Programs

PARI

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

Formula

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

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