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

0,2

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

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

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 *)

Prog

(Magma) [1/4*(n + 1)^2*(n + 2)*(3*n + 2): n in [0..30]]; // Vincenzo Librandi, May 16 2011
(PARI) vector(30, n, n--; (3*n^4+14*n^3+23*n^2+16*n+4)/4) \\ G. C. Greubel, Oct 23 2018
(GAP) List([0..35], n->(1/4)*(n+1)^2*(n+2)*(3*n+2)); # Muniru A Asiru, Oct 24 2018

Crossrefs

Cf. A000217, A000326, A000578, A005915.

Sequence in context: A308596 A145053 A168298 * A241234 A212097 A212098

Adjacent sequences: A126271 A126272 A126273 * A126275 A126276 A126277

Keyword

nonn,easy

Author

Jonathan Vos Post, Mar 09 2007

Extensions

Corrected and extended by Vincenzo Librandi, May 16 2011

Status

approved