A117424 Column 6 of triangle A117418.

1, 7, 37, 180, 871, 4296, 21821, 114676, 624893, 3529464, 20644969, 124886526, 780450996, 5030514429, 33387021887, 227809277707, 1595919320004, 11462822921640, 84307391935729, 634210884766231, 4874831275344622

Offset

0,2

Links

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

Formula

a(n) = A117418(n+6, 6). - 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+6, 6], {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+6, 6) for n in (0..30)] # G. C. Greubel, May 31 2021

Crossrefs

Cf. A117418, A117419, A117420, A117421, A117422, A117423.

Sequence in context: A026862 A026889 A356338 * A192811 A037546 A226867

Adjacent sequences: A117421 A117422 A117423 * A117425 A117426 A117427

Keyword

nonn

Author

Paul D. Hanna, Mar 14 2006

Status

approved