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

0,2

Links

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

Formula

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

Mathematica

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

Prog

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

Crossrefs

Cf. A000522, A228230.

Cf. A368839.

Sequence in context: A059477 A136553 A266293 * A224323 A240650 A356566

Adjacent sequences: A368837 A368838 A368839 * A368841 A368842 A368843

Keyword

nonn,easy

Author

Seiichi Manyama, Jan 07 2024

Status

approved