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A097711 Column 1 of triangle A097710, in which row (n) is formed from the sums of the adjacent terms in row (n-1) of the matrix square of A097710. 2
1, 3, 13, 88, 951, 16691, 484490, 23701698, 1990327810, 291750344191, 75757923092106, 35286335933354828, 29791358931890967248, 45989706937220594708463, 130760311958838053647976497 (list; graph; refs; listen; history; text; internal format)
OFFSET
0,2
COMMENTS
Related to the number of tournament sequences (A008934).
LINKS
MATHEMATICA
T[n_, k_]:= T[n, k]= If[n<0 || k>n, 0, If[n==k, 1, If[k==0, Sum[T[n-1, j]*T[j, 0], {j, 0, n-1}], Sum[T[n-1, j]*(T[j, k-1] +T[j, k]), {j, 0, n-1}] ]]]; (* T = A097710 *)
A097711[n_]:= T[n+1, 1];
Table[A097711[n], {n, 0, 30}] (* G. C. Greubel, Feb 21 2024 *)
PROG
(SageMath)
@CachedFunction
def T(n, k): # T = A097710
if n< 0 or k<0 or k>n: return 0
elif k==n: return 1
elif k==0: return sum(T(n-1, j)*T(j, 0) for j in range(n))
else: return sum(T(n-1, j)*(T(j, k-1)+T(j, k)) for j in range(n))
def A097711(n): return T(n+1, 1)
[A097711(n) for n in range(31)] # G. C. Greubel, Feb 21 2024
CROSSREFS
Sequence in context: A244755 A002725 A324028 * A114477 A345104 A116434
KEYWORD
nonn
AUTHOR
Paul D. Hanna, Aug 22 2004
STATUS
approved

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Last modified April 12 11:25 EDT 2024. Contains 371634 sequences. (Running on oeis4.)