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A368838
a(n) = n! * (n+3)! * Sum_{k=0..n} 1/(k! * (k+3)!).
2
1, 5, 51, 919, 25733, 1029321, 55583335, 3890833451, 342393343689, 36978481118413, 4807202545393691, 740309191990628415, 133255654558313114701, 27717176148129127857809, 6596687923254732430158543, 1781105739278777756142806611, 541456144740748437867413209745
OFFSET
0,2
FORMULA
a(n) = n*(n+3)*a(n-1) + 1.
a(n) ~ BesselI(3,2) * n! * (n+3)!. - Vaclav Kotesovec, Jan 09 2024
PROG
(PARI) a(n) = n!*(n+3)!*sum(k=0, n, 1/(k!*(k+3)!));
CROSSREFS
KEYWORD
nonn,easy
AUTHOR
Seiichi Manyama, Jan 07 2024
STATUS
approved