A189001 a(n) = Sum_{i=0..n} (i+1)*n^i.

1, 3, 17, 142, 1593, 22461, 380713, 7526268, 169826513, 4303999495, 120987654321, 3734729768298, 125562274081225, 4566262891748481, 178581127445062553, 7473240118999870456, 333189190735802745633, 15766036084935301064139

Offset

0,2

Links

Bruno Berselli, Table of n, a(n) for n = 0..300

Formula

a(n) = ((n^2-2)*n^(n+1)+1)/(n-1)^2 for n > 1; a(0)=1, a(1)=3.

Example

a(4) = 1593  because  1593 = 1+2*4+3*4^2+4*4^3+5*4^4.

Mathematica

Join[{1, 3}, Table[(((n^2 - 2) n^(n + 1) + 1) / (n - 1)^2), {n, 2, 20}]] (* Vincenzo Librandi, Aug 19 2013 *)

Prog

(Magma) [&+[(k+1)*n^k: k in [0..n]]: n in [0..17]];

Crossrefs

Cf. A031973, A051846, A062806.

Cf. A189122: Sum_{i=0..n} (i+1)^2*n^i.

Sequence in context: A062873 A120022 A001865 * A087885 A178685 A361767

Adjacent sequences: A188998 A188999 A189000 * A189002 A189003 A189004

Keyword

nonn

Author

Bruno Berselli, Apr 15 2011

Status

approved