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
Keywords
Examples
a(4) = 1593 because 1593 = 1+2*4+3*4^2+4*4^3+5*4^4.
Links
- Bruno Berselli, Table of n, a(n) for n = 0..300
Programs
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Magma
[&+[(k+1)*n^k: k in [0..n]]: n in [0..17]];
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Mathematica
Join[{1, 3}, Table[(((n^2 - 2) n^(n + 1) + 1) / (n - 1)^2), {n, 2, 20}]] (* Vincenzo Librandi, Aug 19 2013 *)
Formula
a(n) = ((n^2-2)*n^(n+1)+1)/(n-1)^2 for n > 1; a(0)=1, a(1)=3.