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 A169938 a(n) = n*(n+1)*(n*(n+1)+1). 6
 0, 0, 6, 42, 156, 420, 930, 1806, 3192, 5256, 8190, 12210, 17556, 24492, 33306, 44310, 57840, 74256, 93942, 117306, 144780, 176820, 213906, 256542, 305256, 360600, 423150, 493506, 572292, 660156, 757770, 865830, 985056, 1116192, 1260006, 1417290, 1588860 (list; graph; refs; listen; history; text; internal format)
 OFFSET -1,3 COMMENTS Partial sums of A061804. - Bruno Berselli, Feb 10 2017 LINKS Vincenzo Librandi, Table of n, a(n) for n = -1..1000 Daniel Poveda Parrilla, Illustration of initial terms seen as cuboids Index entries for linear recurrences with constant coefficients, signature (5,-10,10,-5,1). FORMULA a(n+1) = a(n) + 2(n+1)(2(n+1)^2+1). - Robert Munafo, Jul 27 2010 G.f.: 6*x^2(1 + 2*x + x^2)/(1-x)^5. - Vincenzo Librandi, Dec 18 2012 From Daniel Poveda Parrilla, Jun 08 2017 and Jun 11 2017: (Start) a(n) = A002378(n)*A002061(n+1) for n > -1. a(n) = A002061(A002061(n+1)) - 1. (End) MATHEMATICA CoefficientList[Series[6*x^2(1 + 2*x + x^2)/(1-x)^5, {x, 0, 40}], x] (* Vincenzo Librandi, Dec 18 2012 *) PROG (MAGMA) [n*(n+1)*(n*(n+1)+1): n in [-1..40]]; // Vincenzo Librandi, Dec 18 2012 (PARI) a(n) = n + 2*n^2 + 2*n^3 + n^4; \\ Altug Alkan, Feb 10 2017 (PARI) a(n) = n*=n+1; n*=n+1 \\ David A. Corneth, Jun 11 2017 CROSSREFS A variant of A176780. Cf. A002061, A002378, A061804. A lower bound on A082986. Sequence in context: A046763 A199905 A176780 * A082986 A180806 A253946 Adjacent sequences:  A169935 A169936 A169937 * A169939 A169940 A169941 KEYWORD nonn,easy AUTHOR N. J. A. Sloane, Jul 25 2010, based on an email from Terry Stickel EXTENSIONS The terms were also computed by Robert Munafo, Jul 25 2010 STATUS approved

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Last modified January 27 18:36 EST 2020. Contains 331296 sequences. (Running on oeis4.)