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A117428 Row sums of triangle A117427. 3
1, 3, 9, 30, 110, 442, 1908, 8822, 43330, 224595, 1221860, 6953514, 41232563, 253992215, 1620599471, 10689986451, 72734177909, 509288018981, 3663185604591, 27027424720210, 204246277508032, 1578970198567932 (list; graph; refs; listen; history; text; internal format)
OFFSET
0,2
LINKS
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
Sequence in context: A129167 A151472 A107379 * A339835 A134168 A124427
KEYWORD
nonn
AUTHOR
Paul D. Hanna, Mar 14 2006
STATUS
approved

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Last modified February 28 13:12 EST 2024. Contains 370394 sequences. (Running on oeis4.)