A117426 - OEIS

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

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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.