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

%I A055825 #16 Jan 23 2020 12:33:29
%S A055825 1,5,24,122,640,3422,18536,101362,558336,3093302,17218168,96214890,
%T A055825 539415552,3032659086,17091411912,96527966178,546184965120,
%U A055825 3095613086822,17571039730136,99868193737306,568303494617472
%N A055825 a(n) = T(2n+1,n), array T as in A055818.
%C A055825 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
%H A055825 G. C. Greubel, <a href="/A055825/b055825.txt">Table of n, a(n) for n = 0..250</a>
%p A055825 T:= proc(i, j) option remember;
%p A055825       if i=0 or j=0 then 1
%p A055825     else add(add(T(h,m), m=0..j), h=0..i-1)
%p A055825   fi; end:
%p A055825 seq(T(n+1, n), n=0..30); # _G. C. Greubel_, Jan 22 2020
%t A055825 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 *)
%o A055825 (Sage)
%o A055825 @CachedFunction
%o A055825 def T(i, j):
%o A055825     if (i==0 or j==0): return 1
%o A055825     else: return sum(sum(T(h,m) for m in (0..j)) for h in (0..i-1))
%o A055825 [T(n+1, n) for n in (0..30)] # _G. C. Greubel_, Jan 22 2020
%Y A055825 Cf. A055818, A055819, A055820, A055821, A055822, A055823, A055824, A055826, A055827, A055828, A055829.
%K A055825 nonn
%O A055825 0,2
%A A055825 _Clark Kimberling_, May 28 2000