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

1,2

Links

Robert Israel, Table of n, a(n) for n = 1..364

Eric Weisstein's World of Mathematics, Rising Factorial.

Example

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

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 *)

Prog

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

Crossrefs

Cf. A054654.

Sequence in context: A261065 A071720 A273998 * A302814 A088376 A096293

Adjacent sequences: A111682 A111683 A111684 * A111686 A111687 A111688

Keyword

nonn

Author

Amarnath Murthy, Aug 16 2005

Extensions

More terms from Rick L. Shepherd, Aug 16 2005

Status

approved