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 A117419 Column 1 of triangle A117418; also row sums of triangle A117418; also column 0 of the matrix square of triangle A117418. 7
 1, 2, 4, 9, 23, 66, 209, 724, 2722, 11054, 48221, 224549, 1109099, 5778542, 31599830, 180605495, 1074867618, 6641877098, 42500291654, 280917956734, 1913770121847, 13412187670520, 96528097452230, 712332226596239, 5382561715509704 (list; graph; refs; listen; history; text; internal format)
 OFFSET 0,2 LINKS G. C. Greubel, Table of n, a(n) for n = 0..650 FORMULA a(n) = A117418(n+1, 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[A117418[n+1, 1], {n, 0, 30}] (* G. C. Greubel, May 31 2021 *) PROG (Sage) @CachedFunction def A117418(n, k): if (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)) [A117418(n+1, 1) for n in (0..30)] # G. C. Greubel, May 31 2021 CROSSREFS Cf. A117418, A117420, A117421, A117422, A117423, A117424. Sequence in context: A359032 A129698 A261134 * A124461 A026898 A088930 Adjacent sequences: A117416 A117417 A117418 * A117420 A117421 A117422 KEYWORD nonn AUTHOR Paul D. Hanna, Mar 14 2006 STATUS approved

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Last modified December 7 02:20 EST 2023. Contains 367622 sequences. (Running on oeis4.)