Take the 2-minute tour ×  So I made an error on the question
here: $T_N = 1 + \sum_{k=0}^{N-2}{(N-1-k)T_k}$  The correct
formula I'm trying to solve is more complicated and as follows:
$$T_0 = T_1 = 1 $$  $$T_{N+1} = T_N +
\sum_{k=1}^{N}T_{k-1}T_{N-k}$$  I calculated the first few
terms:  $$T_2 = 2$$  $$T_3 = 2 + T_0T_1 + T_1T_0 = 4$$  $$T_4 =
4 + T_0T_2 + T_1T_1 + T_0T_2 = 4 + 2 + 1 + 2 = 9$$  $$T_5 = 9 +
T_0T_3 + T_1T_2 + T_2T_1 + T_3T_0 = 9 + 4 + 2 + 2 + 4 = 21$$
and plugged it into OEIS and it gave me back:
http://oeis.org/A001006 . Which is exactly the problem I am
trying to solve (non-intersecting chords on a circle).  What I
don't understand is how to use the FORMULA section from OEIS.
Would someone be kind enough to take one of the formulas from
OEIS and walk me through how to use it to actually close my
recurrence, so I can efficiently calculate $T_N$ for large N.
share|improve this question Please avoid using $$ in the title.
–  Asaf Karagila Aug 2 '12 at 2:00 @AsafKaragila: sorry typo – 
Andrew