OFFSET
0,2
COMMENTS
Also the number of binary words with 7n 1's and 7 0's such that for every prefix the number of 1's is >= the number of 0's.
LINKS
Alois P. Heinz, Table of n, a(n) for n = 0..1000
Wikipedia, Young tableau
FORMULA
G.f.: (6*x^7 -48*x^6 +2808*x^5 +83196*x^4 +355384*x^3 +323184*x^2 +58584*x +429)*x / (x-1)^8.
a(n) = C(7*n+7,7)*(7*n-6)/(7*n+1) for n>0, a(0) = 0.
MAPLE
a:= n-> max(0, binomial(7*n+7, 7)*(7*n-6)/(7*n+1)):
seq(a(n), n=0..30);
MATHEMATICA
Join[{0}, Table[Binomial[7n+7, 7] (7n-6)/(7n+1), {n, 30}]] (* Harvey P. Dale, Jul 24 2016 *)
CROSSREFS
KEYWORD
nonn
AUTHOR
Alois P. Heinz, Aug 16 2012
STATUS
approved