A111685 n + n(n+1) + n(n+1)(n+2) + ..., with n terms.

1, 8, 75, 984, 17045, 366288, 9374967, 278095760, 9375293169, 353906211240, 14785127222723, 677150215857192, 33734100501544365, 1816008001717251104, 105048613959883117935, 6497985798745934394528, 427999600108502895779657

Offset: 1

Author

Amarnath Murthy, Aug 16 2005

Keywords

• nonn

Examples

			a(3) = 3+ 3*4 +3*4*5 = 75.
		

Links

• Robert Israel, Table of n, a(n) for n = 1..364
• Eric Weisstein's World of Mathematics, Rising Factorial.

Crossrefs

Cf. A054654.

Programs

Maple

seq(add(pochhammer(n,i),i=1..n),n=1..20); # Robert Israel, Aug 18 2024

Mathematica

Table[Total[Rest[FoldList[Times,1,Range[n,2n-1]]]],{n,20}]  (* Harvey P. Dale, Apr 22 2011 *)
Table[Total[Pochhammer[n, Range[n]]], {n, 20}] (* T. D. Noe, Apr 22 2011 *)

PARI

a(n) = sum(k=0,n-1,prod(j=0,k,n+j)) \\ Rick L. Shepherd, Aug 16 2005

Extensions

More terms from Rick L. Shepherd, Aug 16 2005