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Partial sum of A005915.
5

%I #32 Sep 08 2022 08:45:29

%S 1,15,72,220,525,1071,1960,3312,5265,7975,11616,16380,22477,30135,

%T 39600,51136,65025,81567,101080,123900,150381,180895,215832,255600,

%U 300625,351351,408240,471772,542445,620775,707296,802560,907137,1021615

%N Partial sum of A005915.

%H Vincenzo Librandi, <a href="/A126274/b126274.txt">Table of n, a(n) for n = 0..1000</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) = Sum_{i=0..n} (i + 1)*(3*i^2 + 3*i + 1).

%F a(n) = (3*n^4 + 6*n^3 + 3*n^2)/4 + 2*n^3 + 5*n^2 + 4*n + 1.

%F a(n) = (1/4)*(n + 1)^2*(n + 2)*(3*n + 2). - _N-E. Fahssi_, May 03 2008

%F G.f.: (1 + 10 x + 7 x^2)/(1 - x)^5. - _N-E. Fahssi_, May 03 2008

%F a(n) = (n+1)*A000578(n+1) - Sum_{i=0..n} A000578(i). - _Bruno Berselli_, Apr 24 2010

%F a(n) = Sum_{i=1..n} Sum_{j=1..n} Sum_{k=1..n} max(i,j,k). - _Enrique PĂ©rez Herrero_, Feb 26 2013

%F a(n) = A000217(n+1)*A000326(n+1). - _Bruno Berselli_, Dec 13 2013

%F E.g.f.: (3*x^4 + 32*x^3 + 86*x^2 + 56*x + 4)*exp(x)/4. - _G. C. Greubel_, Oct 23 2018

%p seq(coeff(series((1+10*x+7*x^2)/(1-x)^5,x,n+1), x, n), n = 0 .. 35); # _Muniru A Asiru_, Oct 24 2018

%t Table[(3*n^4 + 14*n^3 + 23*n^2 + 16*n + 4)/4, {n,0,10}] (* _G. C. Greubel_, Oct 23 2018 *)

%t LinearRecurrence[{5,-10,10,-5,1},{1,15,72,220,525},40] (* _Harvey P. Dale_, Mar 31 2022 *)

%o (Magma) [1/4*(n + 1)^2*(n + 2)*(3*n + 2): n in [0..30]]; // _Vincenzo Librandi_, May 16 2011

%o (PARI) vector(30, n, n--; (3*n^4+14*n^3+23*n^2+16*n+4)/4) \\ _G. C. Greubel_, Oct 23 2018

%o (GAP) List([0..35],n->(1/4)*(n+1)^2*(n+2)*(3*n+2)); # _Muniru A Asiru_, Oct 24 2018

%Y Cf. A000217, A000326, A000578, A005915.

%K nonn,easy

%O 0,2

%A _Jonathan Vos Post_, Mar 09 2007

%E Corrected and extended by _Vincenzo Librandi_, May 16 2011