A051053 a(n) = binomial(n, floor(n/6)).

1, 1, 1, 1, 1, 1, 6, 7, 8, 9, 10, 11, 66, 78, 91, 105, 120, 136, 816, 969, 1140, 1330, 1540, 1771, 10626, 12650, 14950, 17550, 20475, 23751, 142506, 169911, 201376, 237336, 278256, 324632, 1947792, 2324784, 2760681, 3262623, 3838380, 4496388

Offset: 0

Author

N. J. A. Sloane

Keywords

• nonn

Links

• Robert Israel, Table of n, a(n) for n = 0..5117

Crossrefs

Cf. A001405, A051033, A051036, A051052.

Programs

Maple

seq(binomial(n, floor(n/6)), n=0..60); # Robert Israel, Mar 11 2018

Mathematica

Table[Binomial[n,Floor[n/6]],{n,0,50}] (* Harvey P. Dale, Dec 18 2013 *)

Formula

From Robert Israel, Mar 11 2018: (Start)

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

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

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