A189122 a(n) = Sum_{i=0..n} (i+1)^2*n^i.
1, 5, 45, 526, 7585, 130371, 2602285, 59142588, 1507308129, 42563286145, 1318792866941, 44477806954890, 1621859437812289, 63576780042697663, 2665971232476845805, 119073945060707737336, 5643402849491554535745
Offset: 0
Examples
a(4) = 7585 because 7585 = 1+2^2*4+3^2*4^2+4^2*4^3+5^2*4^4.
References
- "Supplemento al Periodico di Matematica", Raffaello Giusti Editore (Livorno), Apr/May 1913 p. 99 (Problem 1277, case x=n).
Links
- Bruno Berselli, Table of n, a(n) for n = 0..300
Programs
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Magma
[&+[(k+1)^2*n^k: k in [0..n]]: n in [0..17]];
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Mathematica
Join[{1, 5}, Table[(n + 1) (4 n^(n + 1) - 3 n^(n + 2) - n^(n + 3) + n^(n + 4) -1) / (n - 1)^3, {n, 2, 20}]] (* Vincenzo Librandi, Aug 19 2013 *)
Formula
a(n) = (n+1)*(4*n^(n+1)-3*n^(n+2)-n^(n+3)+n^(n+4)-1)/(n-1)^3 for n>1; a(0)=1, a(1)=5.