A055824 a(n) = T(2*n,n), array T as in A055818.

1, 2, 9, 43, 217, 1131, 6017, 32467, 177009, 972691, 5378425, 29889531, 166795977, 934039419, 5246059761, 29540072355, 166708076001, 942651407907, 5339465635049, 30291114653131, 172081678284729, 978807205953931

Offset: 0

Author

Clark Kimberling, May 28 2000

Keywords

• nonn

Links

• G. C. Greubel, Table of n, a(n) for n = 0..250

Crossrefs

Cf. A055818, A055819, A055820, A055821, A055822, A055823, A055825, A055826, A055827, A055828, A055829.

Programs

Maple

T:= proc(i, j) option remember;
      if i=0 or j=0 then 1
    else add(add(T(h,m), m=0..j), h=0..i-1)
fi; end: seq(T(n, n), n=0..30); # G. C. Greubel, Jan 22 2020

Mathematica

T[i_, j_]:= T[i, j]= If[i==0 || j==0, 1, Sum[T[h, m], {h,0,i-1}, {m,0,j}]]; Table[T[n, n], {n,0,25}] (* G. C. Greubel, Jan 22 2020 *)

Sage

@CachedFunction
def T(i, j):
    if (i==0 or j==0): return 1
    else: return sum(sum(T(h,m) for m in (0..j)) for h in (0..i-1))
[T(n, n) for n in (0..30)] # G. C. Greubel, Jan 22 2020