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%I #6 May 31 2021 21:35:26
%S 1,6,28,126,572,2692,13203,67542,360117,1999817,11541894,69098409,
%T 428183782,2742315847,18117294723,123222721469,861339730328,
%U 6179291890400,45431581077388,341893183760356,2630537501336631
%N Column 5 of triangle A117418.
%H G. C. Greubel, <a href="/A117423/b117423.txt">Table of n, a(n) for n = 0..650</a>
%F a(n) = A117418(n+5, 5). - _G. C. Greubel_, May 31 2021
%t A117418[n_, k_]:= A117418[n, k]= If[k<0 || k>n, 0, If[k==0 || k==n, 1, If[k==n-1, n, Sum[A117418[n -Floor[(k+1)/2], Floor[k/2] +j]*A117418[Floor[(k-1)/2] +j, Floor[(k-1)/2]], {j,0,n-k}] ]]];
%t Table[A117418[n+5,5], {n,0,30}] (* _G. C. Greubel_, May 31 2021 *)
%o (Sage)
%o @CachedFunction
%o def A117418(n, k):
%o if (k==0 or k==n): return 1
%o elif (k==n-1): return n
%o else: return sum( A117418(n -(k+1)//2, k//2 +j)*A117418((k-1)//2 +j, (k-1)//2) for j in (0..n-k))
%o [A117418(n+5, 5) for n in (0..30)] # _G. C. Greubel_, May 31 2021
%Y Cf. A117418, A117419, A117420, A117421, A117422, A117424.
%K nonn
%O 0,2
%A _Paul D. Hanna_, Mar 14 2006
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