A055825 a(n) = T(2n+1,n), array T as in A055818.

1, 5, 24, 122, 640, 3422, 18536, 101362, 558336, 3093302, 17218168, 96214890, 539415552, 3032659086, 17091411912, 96527966178, 546184965120, 3095613086822, 17571039730136, 99868193737306, 568303494617472

Offset: 0

Author

Clark Kimberling, May 28 2000

Keywords

• nonn

Comments

Also main diagonal of array: A(i,1)=i, A(1,j)=j; A(i,j) = 2*A(i,j-1) - A(i-1,j). - Benoit Cloitre, Feb 26 2003

Links

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

Crossrefs

Cf. A055818, A055819, A055820, A055821, A055822, A055823, A055824, 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+1, 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+1, 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+1, n) for n in (0..30)] # G. C. Greubel, Jan 22 2020