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A169938 a(n) = n*(n+1)*(n*(n+1)+1). 6

%I

%S 0,0,6,42,156,420,930,1806,3192,5256,8190,12210,17556,24492,33306,

%T 44310,57840,74256,93942,117306,144780,176820,213906,256542,305256,

%U 360600,423150,493506,572292,660156,757770,865830,985056,1116192,1260006,1417290,1588860

%N a(n) = n*(n+1)*(n*(n+1)+1).

%C Partial sums of A061804. - _Bruno Berselli_, Feb 10 2017

%H Vincenzo Librandi, <a href="/A169938/b169938.txt">Table of n, a(n) for n = -1..1000</a>

%H Daniel Poveda Parrilla, <a href="/A169938/a169938.png">Illustration of initial terms seen as cuboids</a>

%H <a href="/index/Rec#order_05">Index entries for linear recurrences with constant coefficients</a>, signature (5,-10,10,-5,1).

%F a(n+1) = a(n) + 2(n+1)(2(n+1)^2+1). - _Robert Munafo_, Jul 27 2010

%F G.f.: 6*x^2(1 + 2*x + x^2)/(1-x)^5. - _Vincenzo Librandi_, Dec 18 2012

%F From _Daniel Poveda Parrilla_, Jun 08 2017 and Jun 11 2017: (Start)

%F a(n) = A002378(n)*A002061(n+1) for n > -1.

%F a(n) = A002061(A002061(n+1)) - 1. (End)

%t CoefficientList[Series[6*x^2(1 + 2*x + x^2)/(1-x)^5,{x, 0, 40}], x] (* _Vincenzo Librandi_, Dec 18 2012 *)

%o (MAGMA) [n*(n+1)*(n*(n+1)+1): n in [-1..40]]; // _Vincenzo Librandi_, Dec 18 2012

%o (PARI) a(n) = n + 2*n^2 + 2*n^3 + n^4; \\ _Altug Alkan_, Feb 10 2017

%o (PARI) a(n) = n*=n+1;n*=n+1 \\ _David A. Corneth_, Jun 11 2017

%Y A variant of A176780.

%Y Cf. A002061, A002378, A061804.

%Y A lower bound on A082986.

%K nonn,easy

%O -1,3

%A _N. J. A. Sloane_, Jul 25 2010, based on an email from Terry Stickel

%E The terms were also computed by _Robert Munafo_, Jul 25 2010

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Last modified July 15 04:34 EDT 2020. Contains 335763 sequences. (Running on oeis4.)