A117419 Column 1 of triangle A117418; also row sums of triangle A117418; also column 0 of the matrix square of triangle A117418.

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

Offset

0,2

Links

G. C. Greubel, Table of n, a(n) for n = 0..650

Formula

a(n) = A117418(n+1, 1). - G. C. Greubel, May 31 2021

Mathematica

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}] ]]];
Table[A117418[n+1, 1], {n, 0, 30}] (* G. C. Greubel, May 31 2021 *)

Prog

(Sage)
@CachedFunction
def A117418(n, k):
    if (k==0 or k==n): return 1
    elif (k==n-1): return n
    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))
[A117418(n+1, 1) for n in (0..30)] # G. C. Greubel, May 31 2021

Crossrefs

Cf. A117418, A117420, A117421, A117422, A117423, A117424.

Sequence in context: A359032 A129698 A261134 * A124461 A026898 A088930

Adjacent sequences: A117416 A117417 A117418 * A117420 A117421 A117422

Keyword

nonn

Author

Paul D. Hanna, Mar 14 2006

Status

approved