A117423 Column 5 of triangle A117418.

1, 6, 28, 126, 572, 2692, 13203, 67542, 360117, 1999817, 11541894, 69098409, 428183782, 2742315847, 18117294723, 123222721469, 861339730328, 6179291890400, 45431581077388, 341893183760356, 2630537501336631

Offset

0,2

Links

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

Formula

a(n) = A117418(n+5, 5). - 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+5, 5], {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+5, 5) for n in (0..30)] # G. C. Greubel, May 31 2021

Crossrefs

Cf. A117418, A117419, A117420, A117421, A117422, A117424.

Sequence in context: A181337 A002693 A289779 * A351053 A171859 A338584

Adjacent sequences: A117420 A117421 A117422 * A117424 A117425 A117426

Keyword

nonn

Author

Paul D. Hanna, Mar 14 2006

Status

approved