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A097713
Column 1 of triangle A097712.
2
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
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
Sequence in context: A051403 A004205 A268114 * A009392 A130648 A061812
KEYWORD
nonn
AUTHOR
Paul D. Hanna, Aug 24 2004
STATUS
approved