[seqfan] Re: Formulas needed for new sequence.

[Ed Jeffery]

Thanks for those references, Paolo. I'll study them as time permits. If your formula works, then it is a closed form expression.


The range of n for my formula for C_k(n) should have been written as n=k,k+1,k+2,....


Finally, there is an obvious, trivial expression for T(n,k) based on either A056520(n) or A000300(n)+1:


T(n,k)=A056520(n)+k*(n+2)=A000300(n)+k*(n+2)+1, k in {0,...,n}, n>0,

with T(0,0)=1, giving the triangle

1
2, 5,
6, 10, 14,
etc.,

but this is not illuminating.


Ed Jeffery