A117421 - OEIS

%I #6 May 31 2021 21:39:35

%S 1,4,14,50,191,780,3415,15924,78595,408337,2224365,12650992,74876950,

%T 459783611,2922921341,19192162340,129864598566,903840021981,

%U 6460209847133,47345351199234,355305371430875,2727065598788860

%N Column 3 of triangle A117418.

%H G. C. Greubel, <a href="/A117421/b117421.txt">Table of n, a(n) for n = 0..650</a>

%F a(n) = A117418(n+3, 3). - _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+3,3], {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+3, 3) for n in (0..30)] # _G. C. Greubel_, May 31 2021

%Y Cf. A117418, A117419, A117420, A117422, A117423, A117424.

%K nonn

%O 0,2

%A _Paul D. Hanna_, Mar 14 2006