OFFSET
0,2
COMMENTS
Also the number of binary words with 8n 1's and 8 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.: (7*x^8 -63*x^7 -9615*x^6 -572643*x^5 -4331133*x^4 -7786221*x^3 -3699621*x^2 -376497*x -1430)*x / (x-1)^9.
a(n) = C(8*n+8,8)*(8*n-7)/(8*n+1) for n>0, a(0) = 0.
MAPLE
a:= n-> max(0, binomial(8*n+8, 8)*(8*n-7)/(8*n+1)):
seq(a(n), n=0..30);
MATHEMATICA
Join[{0}, Table[(Binomial[8n+8, 8](8n-7))/(8n+1), {n, 20}]] (* Harvey P. Dale, Mar 17 2020 *)
CROSSREFS
KEYWORD
nonn
AUTHOR
Alois P. Heinz, Aug 16 2012
STATUS
approved