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 A117428 Row sums of triangle A117427. 3

%I #6 May 31 2021 05:45:08

%S 1,3,9,30,110,442,1908,8822,43330,224595,1221860,6953514,41232563,

%T 253992215,1620599471,10689986451,72734177909,509288018981,

%U 3663185604591,27027424720210,204246277508032,1578970198567932

%N Row sums of triangle A117427.

%H G. C. Greubel, <a href="/A117428/b117428.txt">Table of n, a(n) for n = 0..650</a>

%F a(n) = Sum_{k=0..n} A117418(n+k+1, 2*k+1). - _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+1, 2*k+1], {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 def A117425(n,k): return A117418(n+k,2*k)

%o [sum(A117418(n+k+1,2*k+1) for k in (0..n)) for n in (0..30)] # _G. C. Greubel_, May 31 2021

%Y Cf. A117418, A117427.

%K nonn

%O 0,2

%A _Paul D. Hanna_, Mar 14 2006

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Last modified April 17 18:43 EDT 2024. Contains 371765 sequences. (Running on oeis4.)