

A117419


Column 1 of triangle A117418; also row sums of triangle A117418; also column 0 of the matrix square of triangle A117418.


7



1, 2, 4, 9, 23, 66, 209, 724, 2722, 11054, 48221, 224549, 1109099, 5778542, 31599830, 180605495, 1074867618, 6641877098, 42500291654, 280917956734, 1913770121847, 13412187670520, 96528097452230, 712332226596239, 5382561715509704
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OFFSET

0,2


LINKS



FORMULA



MATHEMATICA

A117418[n_, k_]:= A117418[n, k]= If[k<0  k>n, 0, If[k==0  k==n, 1, If[k==n1, n, Sum[A117418[n Floor[(k+1)/2], Floor[k/2] +j]*A117418[Floor[(k1)/2] +j, Floor[(k1)/2]], {j, 0, nk}] ]]];


PROG

(Sage)
@CachedFunction
if (k==0 or k==n): return 1
elif (k==n1): return n
else: return sum( A117418(n (k+1)//2, k//2 +j)*A117418((k1)//2 +j, (k1)//2) for j in (0..nk))


CROSSREFS



KEYWORD

nonn


AUTHOR



STATUS

approved



