A117421 Column 3 of triangle A117418.

1, 4, 14, 50, 191, 780, 3415, 15924, 78595, 408337, 2224365, 12650992, 74876950, 459783611, 2922921341, 19192162340, 129864598566, 903840021981, 6460209847133, 47345351199234, 355305371430875, 2727065598788860

Offset

0,2

Links

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

Formula

a(n) = A117418(n+3, 3). - 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+3, 3], {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+3, 3) for n in (0..30)] # G. C. Greubel, May 31 2021

Crossrefs

Cf. A117418, A117419, A117420, A117422, A117423, A117424.

Sequence in context: A076024 A062807 A363507 * A034743 A096241 A283108

Adjacent sequences: A117418 A117419 A117420 * A117422 A117423 A117424

Keyword

nonn

Author

Paul D. Hanna, Mar 14 2006

Status

approved