A051053 - OEIS

%I #12 Mar 11 2018 21:33:08

%S 1,1,1,1,1,1,6,7,8,9,10,11,66,78,91,105,120,136,816,969,1140,1330,

%T 1540,1771,10626,12650,14950,17550,20475,23751,142506,169911,201376,

%U 237336,278256,324632,1947792,2324784,2760681,3262623,3838380,4496388

%N a(n) = binomial(n, floor(n/6)).

%H Robert Israel, <a href="/A051053/b051053.txt">Table of n, a(n) for n = 0..5117</a>

%F From _Robert Israel_, Mar 11 2018: (Start)

%F Let n = 6*k+j, 0 <= j <= 5.

%F a(n+6)*(k+1)*Product_{m=1..5} (5*k+j+m) = a(n)*Product_{m=1..6} (6*k+j+m).

%F a(n) ~ sqrt(3/(5*Pi*k))*(6/5)^j*(6^6/5^5)^k as k -> infinity. (End)

%p seq(binomial(n, floor(n/6)), n=0..60); # _Robert Israel_, Mar 11 2018

%t Table[Binomial[n,Floor[n/6]],{n,0,50}] (* _Harvey P. Dale_, Dec 18 2013 *)

%Y Cf. A001405, A051033, A051036, A051052.

%K nonn

%O 0,7

%A _N. J. A. Sloane_