A152041 a(n) = A008893(n)/2.

0, 4, 33, 129, 355, 795, 1554, 2758, 4554, 7110, 10615, 15279, 21333, 29029, 38640, 50460, 64804, 82008, 102429, 126445, 154455, 186879, 224158, 266754, 315150, 369850, 431379, 500283, 577129, 662505, 757020, 861304, 976008, 1101804, 1239385, 1389465, 1552779

Offset: 0

Author

M. F. Hasler, Sep 15 2009

Keywords

• nonn
• easy

Links

• Nathaniel Johnston, Table of n, a(n) for n = 0..10000
• Index entries for linear recurrences with constant coefficients, signature (5,-10,10,-5,1).

Crossrefs

Cf. A008893.

Programs

Mathematica

Table[n(n+1)(7n^2+7n+2)/8,{n,0,40}] (* or *) LinearRecurrence[ {5,-10,10,-5,1},{0,4,33,129,355},40] (* Harvey P. Dale, Jul 20 2011 *)

Maxima

A152041(n):=n*(n+1)*(7*n^2+7*n+2)/8$
makelist(A152041(n),n,0,30); /* Martin Ettl, Nov 03 2012 */

Formula

a(n) = n*(n+1)*(7*n^2+7*n+2)/8.

G.f.: -x*(4*x^2+13*x+4)/(x-1)^5.

a(n) = 5*a(n-1) - 10*a(n-2) + 10*a(n-3) - 5*a(n-4) + a(n-5). - Harvey P. Dale, Jul 20 2011

E.g.f.: x*(2 + x)*(16 + 42*x + 7*x^2)*exp(x)/8. - Elmo R. Oliveira, Aug 15 2025

Extensions

Extended and edited by Nathaniel Johnston, May 05 2011