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 A172077 n*(n+1)*(7*n^2-n-4)/4. 1

%I

%S 0,1,33,168,520,1245,2541,4648,7848,12465,18865,27456,38688,53053,

%T 71085,93360,120496,153153,192033,237880,291480,353661,425293,507288,

%U 600600,706225,825201,958608,1107568,1273245,1456845,1659616,1882848,2127873

%N n*(n+1)*(7*n^2-n-4)/4.

%C The sequence is related to A172076 by a(n) = n*A172076(n)-sum(A172076(i), i=0..n-1).

%C This is the case d=7 in the identity n*(n*(n+1)*(2*d*n-2*d+3)/6)-sum(k*(k+1)*(2*d*k-2*d+3)/6, k=0..n-1) = n*(n+1)*(3*d*n^2-d*n+4*n-2*d+2)/12. - _Bruno Berselli_, Apr 21 2010

%H Vincenzo Librandi, <a href="/A172077/b172077.txt">Table of n, a(n) for n = 0..1000</a>

%H B. Berselli, A description of the recursive method in Comments lines: website <a href="http://www.lanostra-matematica.org/2008/12/sequenze-numeriche-e-procedimenti.html">Matem@ticamente</a> (in Italian).

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

%F G.f. -x*(1+28*x+13*x^2) / (x-1)^5 . - _R. J. Mathar_, Nov 17 2011

%t CoefficientList[Series[x (1 + 28 x + 13 x^2)/(1 - x)^5, {x, 0, 40}], x] (* _Vincenzo Librandi_, Jan 01 2014 *)

%o (MAGMA) [n*(n+1)*(7*n^2-n-4)/4: n in [0..50]]; // _Vincenzo Librandi_, Jan 01 2014

%Y Cf. A172076.

%K nonn,easy

%O 0,3

%A _Vincenzo Librandi_, Jan 25 2010

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Last modified April 20 17:54 EDT 2019. Contains 322310 sequences. (Running on oeis4.)