30 Jan
2004
30 Jan
'04
1:12 a.m.
Simon> C(n) is slightly lower than 4^n, while the principal term
is 4^n, eventually the sum converge to 2, I am not a combinatorist or a wilf-zeilbergerologist but I can say that there is probably a variety of ways to show that.
My HYPERSIMP Macsyma function can sum Catalan(n)/4^n (without WZ): (c29) (sum(binomial(2*n,n)/(n+1)/4^n,n,0,inf),%% = hypersimp(%%)) inf ==== \ binomial(2 n, n) (d29) > ---------------- = 2 / n ==== 4 (n + 1) n = 0 --rwg