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

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

0,2

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

Links

Harvey P. Dale, Table of n, a(n) for n = 0..1000

Index entries for linear recurrences with constant coefficients, signature (6,-15,20,-15,6,-1,1,-6,15,-20,15,-6,1).

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 *)

Crossrefs

Cf. A032775, A032776.

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).

Sequence in context: A143793 A205818 A259312 * A032776 A251255 A251204

Adjacent sequences: A032771 A032772 A032773 * A032775 A032776 A032777

Keyword

nonn,easy

Author

Patrick De Geest, May 15 1998

Extensions

More terms from Georg Fischer, Feb 23 2021

Status

approved