A172047 n*(n+1)*(15*n^2-n-8)/12.

0, 1, 25, 124, 380, 905, 1841, 3360, 5664, 8985, 13585, 19756, 27820, 38129, 51065, 67040, 86496, 109905, 137769, 170620, 209020, 253561, 304865, 363584, 430400, 506025, 591201, 686700, 793324, 911905, 1043305, 1188416, 1348160, 1523489

Offset: 0

Author

Vincenzo Librandi, Jan 24 2010

Keywords

• nonn
• easy

Comments

This sequence is related to A007587 by a(n) = n*A007587(n)-sum(i=0..n-1, A007587(i)).

This is the case d=5 in the general formula n*(n*(n+1)*(2*d*n-2*d+3)/6)-sum(i=0..n-1, i*(i+1)*(2*d*i-2*d+3)/6) = n*(n+1)*(3*d*n^2-d*n+4*n-2*d+2)/12. - Bruno Berselli, Dec 07 2010

The inverse binomial transform yields 0, 1, 23, 52, 30, 0, 0 (0 continued). - R. J. Mathar, Dec 09 2010

Links

• Vincenzo Librandi, Table of n, a(n) for n = 0..1000
• B. Berselli, A description of the recursive method in Comments lines: website Matem@ticamente (in Italian).
• Index entries for linear recurrences with constant coefficients, signature (5,-10,10,-5,1).

Crossrefs

Cf. A007587.

Programs

Magma

[n*(n+1)*(15*n^2-n-8)/12: n in [0..50]]; // Vincenzo Librandi, Jan 01 2014

Mathematica

CoefficientList[Series[x (1 + 20 x + 9 x^2)/(1 - x)^5, {x, 0, 40}], x] (* Vincenzo Librandi, Jan 01 2014 *)

Formula

G.f.: -x*(1+20*x+9*x^2)/(x-1)^5. - R. J. Mathar, Dec 09 2010

a(n)-a(-n) = A063521(n). - Bruno Berselli, Aug 26 2011