A117424 - OEIS

A117424

Column 6 of triangle A117418.

1, 7, 37, 180, 871, 4296, 21821, 114676, 624893, 3529464, 20644969, 124886526, 780450996, 5030514429, 33387021887, 227809277707, 1595919320004, 11462822921640, 84307391935729, 634210884766231, 4874831275344622

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OFFSET

0,2

LINKS

G. C. Greubel, Table of n, a(n) for n = 0..650

FORMULA

a(n) = A117418(n+6, 6). - 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+6, 6], {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+6, 6) for n in (0..30)] # G. C. Greubel, May 31 2021

CROSSREFS

Cf. A117418, A117419, A117420, A117421, A117422, A117423.

Sequence in context: A026862 A026889 A356338 * A192811 A037546 A226867

Adjacent sequences: A117421 A117422 A117423 * A117425 A117426 A117427

KEYWORD

nonn

AUTHOR

Paul D. Hanna, Mar 14 2006

STATUS

approved