A093657 2^(n-1)-th term of the row sums of triangle A093654.

1, 2, 6, 28, 206, 2418, 45970, 1440746, 75840096, 6828414424, 1069361760254, 295609883371824, 146078092162147126, 130419475982163166640, 212257994312591826735888, 634463537260289571176650942

Offset: 1

Author

Paul D. Hanna, Apr 08 2004

Keywords

• nonn

Links

• G. C. Greubel, Table of n, a(n) for n = 1..86

Crossrefs

Cf. A093654, A093656.

Related to the number of tournament sequences (A008934).

Cf. A097710, A008934.

Programs

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 *)

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

Formula

a(n) = A093656(2^(n-1)) for n>=1.

a(n) = Sum_{k=0..n} A097710(n,k), row sums of triangle A097710.