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 1-3 of 3 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

A032779 Integer quotients n(n+1)(n+2)...(n+7) / (n+(n+1)+(n+2)+...+(n+7)).

Original entry on oeis.org

0, 1120, 110880, 1441440, 5189184, 58605120, 349949600, 639381600, 3765731200, 12841684128, 136367431200, 1442885004000, 4895245266912, 28461435424576, 51671930508000, 300266024938880, 3166522452945280, 10732052830603104
Offset: 1

Views

Author

Patrick De Geest, May 15 1998

Keywords

Crossrefs

Extensions

Offset and a(14) corrected by Sean A. Irvine, Jun 25 2020

A032778 Numbers k such that k*(k+1)*(k+2)*...*(k+7) / (k+(k+1)+(k+2)+...+(k+7)) is an integer.

Original entry on oeis.org

0, 1, 4, 7, 9, 14, 19, 21, 28, 34, 49, 70, 84, 109, 119, 154, 217, 259, 364, 609, 784, 1099, 1834, 5509
Offset: 1

Views

Author

Patrick De Geest, May 15 1998

Keywords

Comments

(d-7)/2 where d >= 7 is a divisor of 11025, so sequence is finite. - Robert Israel, Jul 12 2018

Crossrefs

Programs

  • Mathematica
    Select[Range[0, 300], IntegerQ[Times@@Range[#, # + 7] / Total[Range[#, # + 7]]] &] (* Vincenzo Librandi, Jul 13 2018 *)

Extensions

Offset changed by Robert Israel, Jul 12 2018
Showing 1-3 of 3 results.