A189122 - OEIS

%I #18 Sep 08 2022 08:45:56

%S 1,5,45,526,7585,130371,2602285,59142588,1507308129,42563286145,

%T 1318792866941,44477806954890,1621859437812289,63576780042697663,

%U 2665971232476845805,119073945060707737336,5643402849491554535745

%N a(n) = Sum_{i=0..n} (i+1)^2*n^i.

%D "Supplemento al Periodico di Matematica", Raffaello Giusti Editore (Livorno), Apr/May 1913 p. 99 (Problem 1277, case x=n).

%H Bruno Berselli, <a href="/A189122/b189122.txt">Table of n, a(n) for n = 0..300</a>

%F 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.

%e a(4) = 7585  because  7585 = 1+2^2*4+3^2*4^2+4^2*4^3+5^2*4^4.

%t 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 *)

%o (Magma) [&+[(k+1)^2*n^k: k in [0..n]]: n in [0..17]];

%Y Cf. A062806, A189001.

%K nonn,easy

%O 0,2

%A _Bruno Berselli_, Apr 19 2011