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

0,2

Comments

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

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).

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

Example

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.

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 *)

Prog

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

Crossrefs

Cf. A213821.

Sequence in context: A212501 A117717 A359252 * A168172 A127305 A363753

Adjacent sequences: A176057 A176058 A176059 * A176061 A176062 A176063

Keyword

nonn,easy

Author

Bruno Berselli, Dec 06 2010

Status

approved