
COMMENTS

No formula is presently known.
From Colin Defant, Aug 16 2016: (Start)
For each subset W={w_1,w_2,...,w_k} of {n+1,n+2,...,2n} satisfying w_1<w_2<...<w_k, let H(W) be the number of sequences of integers i_1,i_2,...,i_k such that i_1<i_2<...<i_k and w_jn+j<=i_j<=w_j1 for all j. We have a(n)=Sum(H(W)), where the sum ranges over all subsets W of {n+1,n+2,...,2n}.
3 + sqrt(8) <= lim_(n>oo)a(n)^(1/n) <= 27/4. (End)
