A093657 - OEIS

The OEIS is supported by the many generous donors to the OEIS Foundation.

Year-end appeal: Please make a donation to the OEIS Foundation to support ongoing development and maintenance of the OEIS. We are now in our 61st year, we have over 378,000 sequences, and we’ve reached 11,000 citations (which often say “discovered thanks to the OEIS”).

Other ways to Give

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

(list; graph; refs; listen; history; text; internal format)

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