A176060 a(n) = n*(n+1)*(3*n^2+5*n+4)/12.

0, 2, 13, 46, 120, 260, 497, 868, 1416, 2190, 3245, 4642, 6448, 8736, 11585, 15080, 19312, 24378, 30381, 37430, 45640, 55132, 66033, 78476, 92600, 108550, 126477, 146538, 168896, 193720, 221185, 251472, 284768, 321266, 361165, 404670, 451992

Offset: 0

Author

Bruno Berselli, Dec 06 2010

Keywords

• nonn
• easy

Comments

Antidiagonal sums of the convolution array A213821. [Clark Kimberling, Jul 04 2012]

Examples

			For n=5, a(5)=1*(1*0+6)+2*(2*1+6)+3*(3*2+6)+4*(4*3+6)+5*(5*4+6)=260.
		

References

• "Supplemento al Periodico di Matematica", Raffaello Giusti Editore (Livorno), May 1908, p. 111 (Problem 923).

Links

• Vincenzo Librandi, 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. A213821.

Programs

Magma

[n*(n+1)*(3*n^2+5*n+4)/12: n in [0..40]]; // Vincenzo Librandi, Jul 02 2011

Mathematica

Table[n(n+1)(3n^2+5n+4)/12,{n,0,40}] (* or *) LinearRecurrence[ {5,-10,10,-5,1},{0,2,13,46,120},40] (* Harvey P. Dale, Jul 14 2011 *)

Formula

G.f.: x*(2+3*x+x^2)/(1-x)^5.

a(n) = sum(k*(k*(k-1)+n+1), k=1..n) with n>0 (summation proposed in the Problem 923, see References).

a(0)=0, a(1)=2, a(2)=13, a(3)=46, a(4)=120, 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 14 2011

a(-n) = A132117(n-1) with A132117(-1)=A132117(0)=0. - Bruno Berselli, Aug 22 2011