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A093657
2^(n-1)-th term of the row sums of triangle A093654.
3
1, 2, 6, 28, 206, 2418, 45970, 1440746, 75840096, 6828414424, 1069361760254, 295609883371824, 146078092162147126, 130419475982163166640, 212257994312591826735888, 634463537260289571176650942
OFFSET
1,2
LINKS
FORMULA
a(n) = A093656(2^(n-1)) for n>=1.
a(n) = Sum_{k=0..n} A097710(n,k), row sums of triangle A097710.
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 *)
A093657[n_]:= A093657[n]= Sum[T[n, k], {k, 0, n}];
Table[A093657[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 A093657(n): return sum(T(n, k) for k in range(n+1))
[A093657(n) for n in range(31)] # G. C. Greubel, Feb 21 2024
CROSSREFS
Related to the number of tournament sequences (A008934).
Sequence in context: A324126 A272662 A125812 * A355064 A305627 A006117
KEYWORD
nonn
AUTHOR
Paul D. Hanna, Apr 08 2004
STATUS
approved