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.

1, 3, 13, 88, 951, 16691, 484490, 23701698, 1990327810, 291750344191, 75757923092106, 35286335933354828, 29791358931890967248, 45989706937220594708463, 130760311958838053647976497

Offset: 0

Author

Paul D. Hanna, Aug 22 2004

Keywords

• nonn

Comments

Related to the number of tournament sequences (A008934).

Links

• G. C. Greubel, Table of n, a(n) for n = 0..84

Crossrefs

Cf. A008934, A097710.

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 *)
A097711[n_]:= T[n+1,1];
Table[A097711[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 A097711(n): return T(n+1,1)
[A097711(n) for n in range(31)] # G. C. Greubel, Feb 21 2024