A147631 9-factorial numbers (6).

1, 7, 112, 2800, 95200, 4093600, 212867200, 12984899200, 908942944000, 71806492576000, 6318971346688000, 612940220628736000, 64971663386646016000, 7471741289464291840000, 926495919893572188160000, 123223957345845101025280000, 17497801943110004345589760000

Offset: 1

Author

Vladimir Joseph Stephan Orlovsky, Nov 08 2008

Keywords

• nonn

Crossrefs

Cf. A147630, A147629, A049211, A051232, A045756, A035012, A035013, A035017, A035018, A035020, A035022, A035023, A053116.

Cf. A048994, A132393.

Programs

Mathematica

s=1;lst={s};Do[s+=n*s;AppendTo[lst,s],{n,6,2*5!,9}];lst

Formula

a(n+1) = Sum_{k=0..n} A132393(n,k)*7^k*9^(n-k). - Philippe Deléham, Nov 09 2008

a(n) = (-2)^n*Sum_{k=0..n} (9/2)^k*s(n+1,n+1-k), where s(n,k) are the Stirling numbers of the first kind, A048994. - Mircea Merca, May 03 2012

Sum_{n>=1} 1/a(n) = 1 + (e/9^2)^(1/9)*(Gamma(7/9) - Gamma(7/9, 1/9)). - Amiram Eldar, Dec 21 2022