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

1,2

Links

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

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

Cf. A093654, A093656.

Related to the number of tournament sequences (A008934).

Cf. A097710, A008934.

Sequence in context: A324126 A272662 A125812 * A355064 A305627 A006117

Adjacent sequences: A093654 A093655 A093656 * A093658 A093659 A093660

Keyword

nonn

Author

Paul D. Hanna, Apr 08 2004

Status

approved