A117426 Row sums of triangle A117425.

1, 2, 5, 15, 51, 192, 781, 3416, 15925, 78596, 408338, 2224366, 12650993, 74876951, 459783612, 2922921342, 19192162341, 129864598567, 903840021982, 6460209847134, 47345351199235, 355305371430876, 2727065598788861

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, 2*k). - 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, 2*k], {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))
[sum(A117418(n+k, 2*k) for k in (0..n)) for n in (0..40)] # G. C. Greubel, May 31 2021

Crossrefs

Cf. A117418, A117425.

Sequence in context: A193296 A304454 A287253 * A201168 A001681 A343665

Adjacent sequences: A117423 A117424 A117425 * A117427 A117428 A117429

Keyword

nonn

Author

Paul D. Hanna, Mar 14 2006

Status

approved