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%I #6 May 31 2021 21:45:36
%S 1,3,8,22,65,208,723,2721,11053,48220,224548,1109098,5778541,31599829,
%T 180605494,1074867617,6641877097,42500291653,280917956733,
%U 1913770121846,13412187670519,96528097452229,712332226596238,5382561715509703
%N Column 2 of triangle A117418.
%H G. C. Greubel, <a href="/A117420/b117420.txt">Table of n, a(n) for n = 0..650</a>
%F a(n) = A117418(n+2, 2). - _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+2,2], {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+2, 2) for n in (0..30)] # _G. C. Greubel_, May 31 2021
%Y Cf. A117418, A117419, A117421, A117422, A117423, A117424.
%K nonn
%O 0,2
%A _Paul D. Hanna_, Mar 14 2006
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