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

%I A055824 #12 Jan 23 2020 12:30:37
%S A055824 1,2,9,43,217,1131,6017,32467,177009,972691,5378425,29889531,
%T A055824 166795977,934039419,5246059761,29540072355,166708076001,942651407907,
%U A055824 5339465635049,30291114653131,172081678284729,978807205953931
%N A055824 a(n) = T(2*n,n), array T as in A055818.
%H A055824 G. C. Greubel, <a href="/A055824/b055824.txt">Table of n, a(n) for n = 0..250</a>
%p A055824 T:= proc(i, j) option remember;
%p A055824       if i=0 or j=0 then 1
%p A055824     else add(add(T(h,m), m=0..j), h=0..i-1)
%p A055824 fi; end: seq(T(n, n), n=0..30); # _G. C. Greubel_, Jan 22 2020
%t A055824 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 *)
%o A055824 (Sage)
%o A055824 @CachedFunction
%o A055824 def T(i, j):
%o A055824     if (i==0 or j==0): return 1
%o A055824     else: return sum(sum(T(h,m) for m in (0..j)) for h in (0..i-1))
%o A055824 [T(n, n) for n in (0..30)] # _G. C. Greubel_, Jan 22 2020
%Y A055824 Cf. A055818, A055819, A055820, A055821, A055822, A055823, A055825, A055826, A055827, A055828, A055829.
%K A055824 nonn
%O A055824 0,2
%A A055824 _Clark Kimberling_, May 28 2000