A126274 Partial sum of A005915.

1, 15, 72, 220, 525, 1071, 1960, 3312, 5265, 7975, 11616, 16380, 22477, 30135, 39600, 51136, 65025, 81567, 101080, 123900, 150381, 180895, 215832, 255600, 300625, 351351, 408240, 471772, 542445, 620775, 707296, 802560, 907137, 1021615

Offset: 0

Author

Jonathan Vos Post, Mar 09 2007

Keywords

• nonn
• easy

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).

Crossrefs

Cf. A000217, A000326, A000578, A005915.

Programs

GAP

List([0..35],n->(1/4)*(n+1)^2*(n+2)*(3*n+2)); # Muniru A Asiru, Oct 24 2018

Magma

[1/4*(n + 1)^2*(n + 2)*(3*n + 2): n in [0..30]]; // Vincenzo Librandi, May 16 2011

Maple

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

Mathematica

Table[(3*n^4 + 14*n^3 + 23*n^2 + 16*n + 4)/4, {n,0,10}] (* G. C. Greubel, Oct 23 2018 *)
LinearRecurrence[{5,-10,10,-5,1},{1,15,72,220,525},40] (* Harvey P. Dale, Mar 31 2022 *)

PARI

vector(30, n, n--; (3*n^4+14*n^3+23*n^2+16*n+4)/4) \\ G. C. Greubel, Oct 23 2018

Formula

a(n) = Sum_{i=0..n} (i + 1)*(3*i^2 + 3*i + 1).

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

a(n) = (1/4)*(n + 1)^2*(n + 2)*(3*n + 2). - N-E. Fahssi, May 03 2008

G.f.: (1 + 10 x + 7 x^2)/(1 - x)^5. - N-E. Fahssi, May 03 2008

a(n) = (n+1)*A000578(n+1) - Sum_{i=0..n} A000578(i). - Bruno Berselli, Apr 24 2010

a(n) = Sum_{i=1..n} Sum_{j=1..n} Sum_{k=1..n} max(i,j,k). - Enrique Pérez Herrero, Feb 26 2013

a(n) = A000217(n+1)*A000326(n+1). - Bruno Berselli, Dec 13 2013

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

Extensions

Corrected and extended by Vincenzo Librandi, May 16 2011