A117420 Column 2 of triangle A117418.

1, 3, 8, 22, 65, 208, 723, 2721, 11053, 48220, 224548, 1109098, 5778541, 31599829, 180605494, 1074867617, 6641877097, 42500291653, 280917956733, 1913770121846, 13412187670519, 96528097452229, 712332226596238, 5382561715509703

Offset

0,2

Links

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

Formula

a(n) = A117418(n+2, 2). - 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+2, 2], {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+2, 2) for n in (0..30)] # G. C. Greubel, May 31 2021

Crossrefs

Cf. A117418, A117419, A117421, A117422, A117423, A117424.

Sequence in context: A099324 A372528 A290898 * A003101 A064443 A000732

Adjacent sequences: A117417 A117418 A117419 * A117421 A117422 A117423

Keyword

nonn

Author

Paul D. Hanna, Mar 14 2006

Status

approved