A097713 Column 1 of triangle A097712.

1, 3, 8, 25, 111, 809, 10360, 236952, 9708797, 714862984, 95000655195, 22902964060238, 10070812803900694, 8120691251242651341, 12070960239863869828931, 33238610095183531376362138

Offset

0,2

Comments

Partial sums of A016121.

The row sums of triangle A097712 give A016121.

Links

G. C. Greubel, Table of n, a(n) for n = 0..85

Formula

a(n) = Sum_{k=0..n} A016121(k).

Mathematica

T[n_, k_]:= T[n, k]= If[n<0 || k>n, 0, If[k==0 || k==n, 1, T[n-1, k] + Sum[T[n-1, j]*T[j, k-1], {j, 0, n-1}] ]]; (* T=A097712 *)
A097713[n_]:= T[n, 1];
Table[A097713[n], {n, 30}] (* G. C. Greubel, Feb 22 2024 *)

Prog

(SageMath)
@CachedFunction
def T(n, k): # T = A097712
    if k<0 or k>n: return 0
    elif k==0 or k==n: return 1
    else: return T(n-1, k) + sum(T(n-1, j)*T(j, k-1) for j in range(n))
def A097713(n): return T(n, 1)
[A097713(n) for n in range(1, 31)] # G. C. Greubel, Feb 22 2024

Crossrefs

Cf. A016121, A097712.

Sequence in context: A051403 A004205 A268114 * A009392 A130648 A061812

Adjacent sequences: A097710 A097711 A097712 * A097714 A097715 A097716

Keyword

nonn

Author

Paul D. Hanna, Aug 24 2004

Status

approved