A368840 a(n) = n! * (n+1)! * (n+2)! * Sum_{k=0..n} 1/(6^(n-k) * k! * (k+1)! * (k+2)!).

1, 2, 9, 91, 1821, 63736, 3569217, 299814229, 35977707481, 5936321734366, 1305990781560521, 373513363526309007, 135958864323576478549, 61861283267227297739796, 34642318629647286734285761, 23556776668160154979314317481

Offset: 0

Author

Seiichi Manyama, Jan 07 2024

Keywords

• nonn
• easy

Links

• Harvey P. Dale, Table of n, a(n) for n = 0..203

Crossrefs

Cf. A000522, A228230.

Cf. A368839.

Programs

Mathematica

nxt[{n_,a_}]:={n+1,a*Binomial[n+3,3]+1}; NestList[nxt,{0,1},20][[;;,2]] (* Harvey P. Dale, May 26 2024 *)

PARI

a(n) = n!*(n+1)!*(n+2)!*sum(k=0, n, 1/(6^(n-k)*k!*(k+1)!*(k+2)!));

Formula

a(n) = binomial(n+2,3)*a(n-1) + 1.