A063521 -id:A063521 - cp's OEIS frontend

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

Vincenzo Librandi, Jan 24 2010

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

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).

Cf. A007587.

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

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

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

cp's OEIS Frontend

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

Views

Author

Keywords

Comments

Links

Crossrefs

Programs

Magma

Mathematica

Formula