The OEIS mourns the passing of Jim Simons and is grateful to the Simons Foundation for its support of research in many branches of science, including the OEIS.
The OEIS is supported by the many generous donors to the OEIS Foundation.

 Hints (Greetings from The On-Line Encyclopedia of Integer Sequences!)
 A117426 Row sums of triangle A117425. 2

%I #8 May 31 2021 13:39:56

%S 1,2,5,15,51,192,781,3416,15925,78596,408338,2224366,12650993,

%T 74876951,459783612,2922921342,19192162341,129864598567,903840021982,

%U 6460209847134,47345351199235,355305371430876,2727065598788861

%N Row sums of triangle A117425.

%H G. C. Greubel, <a href="/A117426/b117426.txt">Table of n, a(n) for n = 0..650</a>

%F a(n) = Sum_{k=0..n} A117418(n+k, 2*k). - _G. C. Greubel_, May 31 2021

%t 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}]]]];

%t Table[Sum[A117418[n+k, 2*k], {k,0,n}], {n,0,40}] (* _G. C. Greubel_, May 31 2021 *)

%o (Sage)

%o @CachedFunction

%o def A117418(n, k):

%o if (k<0 or k>n): return 0

%o elif (k==0 or k==n): return 1

%o elif (k==n-1): return n

%o 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))

%o [sum(A117418(n+k,2*k) for k in (0..n)) for n in (0..40)] # _G. C. Greubel_, May 31 2021

%Y Cf. A117418, A117425.

%K nonn

%O 0,2

%A _Paul D. Hanna_, Mar 14 2006

Lookup | Welcome | Wiki | Register | Music | Plot 2 | Demos | Index | Browse | More | WebCam
Contribute new seq. or comment | Format | Style Sheet | Transforms | Superseeker | Recents
The OEIS Community | Maintained by The OEIS Foundation Inc.

Last modified May 28 19:55 EDT 2024. Contains 372919 sequences. (Running on oeis4.)