A117428 Row sums of triangle A117427.

1, 3, 9, 30, 110, 442, 1908, 8822, 43330, 224595, 1221860, 6953514, 41232563, 253992215, 1620599471, 10689986451, 72734177909, 509288018981, 3663185604591, 27027424720210, 204246277508032, 1578970198567932

Offset

0,2

Links

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

Formula

a(n) = Sum_{k=0..n} A117418(n+k+1, 2*k+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[Sum[A117418[n+k+1, 2*k+1], {k, 0, n}], {n, 0, 40}] (* G. C. Greubel, May 31 2021 *)

Prog

(Sage)
@CachedFunction
def A117418(n, k):
    if (k<0 or k>n): return 0
    elif (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))
def A117425(n, k): return A117418(n+k, 2*k)
[sum(A117418(n+k+1, 2*k+1) for k in (0..n)) for n in (0..30)] # G. C. Greubel, May 31 2021

Crossrefs

Cf. A117418, A117427.

Sequence in context: A129167 A151472 A107379 * A339835 A134168 A124427

Adjacent sequences: A117425 A117426 A117427 * A117429 A117430 A117431

Keyword

nonn

Author

Paul D. Hanna, Mar 14 2006

Status

approved