A027686 - cp's OEIS frontend

A027686 Number of ways to transform say (((((((ab)c)d)e)f)g)h) to (a(b(c(d(e(f(gh))))))) where there are n multiplications (hence n+1 variables) by repeatedly applying the one-way associative law ((xy)z) -> (x(yz)).

n	a(n)
0	1
1	1
2	1
3	2
4	9
5	98
6	2981
7	340549
8	216569887
9	994441978397
10	36812710172987995
11	12001387004225881846755
12	37783429241635794906272195147
13	1255674108542254217846031366276646429
14	478743486470659944952229546087586449114251007
15	2262324605850021060149051111359520226936424091385392945

[1, 1, 1, 2, 9, 98, 2981, 340549, 216569887, 994441978397, 36812710172987995, 12001387004225881846755, 37783429241635794906272195147, 1255674108542254217846031366276646429, 478743486470659944952229546087586449114251007, 2262324605850021060149051111359520226936424091385392945]

cp's OEIS Frontend

A027686 Number of ways to transform say (((((((ab)c)d)e)f)g)h) to (a(b(c(d(e(f(gh))))))) where there are n multiplications (hence n+1 variables) by repeatedly applying the one-way associative law ((xy)z) -> (x(yz)).

Table of values

List of values