cp's OEIS Frontend

This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.

Showing 1-1 of 1 results.

A032774 a(n) = floor( n*(n+1)*(n+2)*...*(n+6) / (n+(n+1)+(n+2)+...+(n+6)) ).

Original entry on oeis.org

0, 180, 1152, 4320, 12342, 29700, 63360, 123552, 224640, 386100, 633600, 1000182, 1527552, 2267460, 3283200, 4651200, 6462720, 8825652, 11866422, 15732000, 20592000, 26640900, 34100352, 43221600, 54288000, 67617642, 83566080, 102529152, 124945920, 151301700, 182131200
Offset: 0

Views

Author

Patrick De Geest, May 15 1998

Keywords

Comments

In general, such sequences a(n) = floor((Product_{m=0..k} n+i) / (Sum_{m=0..k} n+i)) have rational generating functions. - Georg Fischer, Feb 23 2021

Crossrefs

Cf. A004526 (k=2), A032765 (k=3), A032768 (k=4), A032771 (k=5), A032774 (k=6), A032777 (k=7), A032780 (k=8), A032790 (k=9).

Programs

  • Maple
    seq(coeff(series( -(6*x^10-36*x^9 + 90*x^8 - 120*x^7 - 90*x^6 - 108*x^5 - 102*x^4 - 108*x^3 - 72*x^2 - 180*x) / (-x^13+6*x^12 - 15*x^11+20*x^10 - 15*x^9+6*x^8 - x^7+x^6 - 6*x^5+15*x^4 - 20*x^3+15*x^2 - 6*x + 1) , x, n+1), x, n), n = 0..40); # Georg Fischer, Feb 23 2021
  • Mathematica
    Table[Floor[(Times @@ Range[n, n + 6])/(7 n + 21)], {n, 0, 30}] (* Harvey P. Dale, May 16 2020 *)

Extensions

More terms from Georg Fischer, Feb 23 2021
Showing 1-1 of 1 results.