A109398 a(n) = (1/n!)*Sum_{k=0..n} (n+k)!.

1, 3, 16, 145, 1926, 33649, 726328, 18636561, 553680370, 18684924841, 705833193924, 29502690532393, 1351724235304366, 67359683340291105, 3627011494019437936, 209846445862386234529, 12982402818188717219658

Offset: 0

Author

Vladeta Jovovic, Aug 26 2005

Keywords

• easy
• nonn

Crossrefs

Cf. A111686.

Programs

Mathematica

Table[Sum[Binomial[n+k,k]k!,{k,0,n}],{n,0,100}] (* Emanuele Munarini, Sep 20 2016 *)

Maxima

makelist(sum(binomial(n+k,k)*k!,k,0,n),n,0,12); /* Emanuele Munarini, Sep 20 2016 */

Formula

a(n) ~ 2^(2*n + 1/2) * n^n / exp(n). - Vaclav Kotesovec, Nov 27 2017