A185009 Row sums of A051949 (differences of factorial numbers), seen as a triangle.

0, 5, 45, 351, 2847, 25047, 241047, 2534247, 28984167, 358842087, 4785978087, 68453274087, 1045616538087, 16993016806887, 292825130163687, 5333909818803687, 102415654899123687, 2067588695129523687, 43785455761653171687, 970599475776544179687

Offset: 1

Author

Olivier Gérard, Nov 02 2012

Keywords

• nonn
• easy

Links

• G. C. Greubel, Table of n, a(n) for n = 1..445

Crossrefs

cf. A051949.

Other summations of differences of factorials : A206816, A206817, A065355.

Programs

Mathematica

Table[Plus @@ Prepend[Table[(n + 1)! - i!, {i, n, 2, -1}], (n)! - 1], {n, 0, 20}]

PARI

for(n=1,25, print1((n^2-1)*n! - sum(k=1,n-1, k!), ", ")) \\ G. C. Greubel, Jun 09 2017

Formula

a(n)= (n-1)*(n+1)*n! - sum( i!, i=1..n-1)