A368839 -id:A368839 - cp's OEIS frontend

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

Seiichi Manyama, Jan 07 2024

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

Cf. A000522, A228230.

Cf. A368839.

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

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

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

A368854 a(n) = n! * (n+1)! * (n+2)! * Sum_{k=0..n} (-1)^k/(k! * (k+1)! * (k+2)!).

Original entry on oeis.org

1, 5, 121, 7259, 871081, 182927009, 61463475025, 30977591412599, 22303865817071281, 22080827158900568189, 29146691849748750009481, 50015723214168855016269395, 109234339499744779355532358681, 298209746834303247640603339199129

Offset: 0

Seiichi Manyama, Jan 07 2024

Cf. A000166, A368853.

Cf. A368839.

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

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

a(n) ~ c * n!*(n+1)!*(n+2)!, where c = hypergeom([], [2, 3], -1)/2 = 0.42008149848198278018826635149001977031641229888902795699817... - Vaclav Kotesovec, Jan 08 2024

cp's OEIS Frontend

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

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