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 A172118 n*(n+1)*(5*n^2-n-3)/2. 1
 0, 1, 45, 234, 730, 1755, 3591, 6580, 11124, 17685, 26785, 39006, 54990, 75439, 101115, 132840, 171496, 218025, 273429, 338770, 415170, 503811, 605935, 722844, 855900, 1006525, 1176201, 1366470, 1578934, 1815255, 2077155, 2366416, 2684880 (list; graph; refs; listen; history; text; internal format)
 OFFSET 0,3 COMMENTS a(n) = n*(n*(n+1)*(20*n-17)/6) - sum( i*(i+1)*(20*i-17)/2, i=0..n-1 ) = n*(n+1)*(5*n^2-n-3)/2. More generally: n*(n*(n+1)*(2*d*n-2*d+3)/6) - sum( i*(i+1)*(2*d*i-2*d+3)/6, i=0..n-1 ) = n*(n+1)*(3*d*n^2-d*n+4*n-2*d+2)/12; in this sequence is d=10. - Bruno Berselli, May 07 2010 LINKS Vincenzo Librandi, Table of n, a(n) for n = 0..1000 Index entries for linear recurrences with constant coefficients, signature (5,-10,10,-5,1). FORMULA G.f. -x*(1+40*x+19*x^2) / (x-1)^5 . - R. J. Mathar, Nov 17 2011 MATHEMATICA Table[n*(n + 1)*(5*n^2 - n - 3)/2, {n, 0, 40}] (* or *) CoefficientList[Series[-x (1 + 40 x + 19 x^2)/(x - 1)^5, {x, 0, 40}], x] (* Vincenzo Librandi, Aug 20 2014 *) PROG (MAGMA) [n*(n+1)*(5*n^2-n-3)/2: n in [0..50]]; // Vincenzo Librandi, Aug 20 2014 CROSSREFS Cf. A172117. Sequence in context: A251444 A169717 A246420 * A127073 A089549 A178540 Adjacent sequences:  A172115 A172116 A172117 * A172119 A172120 A172121 KEYWORD nonn,easy AUTHOR Vincenzo Librandi, Jan 26 2010 EXTENSIONS Simplified formula and corrected sequence A172117 by Bruno Berselli, May 07 2010 STATUS approved

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