missing table -- "Unexpected error." on Lookup
Paul D. Hanna
pauldhanna at juno.com
Tue Dec 12 07:09:20 CET 2006
Neil,
The sequences: A045501, A045499, A045500,
return: "Unexpected error."
Perhaps you are aware of this?
> there was a discussion here in November about this.
> based on emails from Emeric, Paul H. and especially Richard Mathar,
> I'm
> adding the missing entry as A121207.
> Neil
Also, following is an observation regarding A121207 worth sharing.
Consider the row reversal of triangle A121207;
of course, the resultant triangle equals Emeric's triangle A124496
with an additional left column (=A000110 Bell numbers).
What is interesting is the simplicity of the matrix inverse.
The matrix inverse of the row-reversal of A121207 begins:
1;
-1, 1;
-1, -1, 1;
-1, -2, -1, 1;
-1, -3, -3, -1, 1;
-1, -4, -6, -4, -1, 1;
-1, -5, -10, -10, -5, -1, 1;
-1, -6, -15, -20, -15, -6, -1, 1;
-1, -7, -21, -35, -35, -21, -7, -1, 1;
-1, -8, -28, -56, -70, -56, -28, -8, -1, 1; ...
This gives the recurrence and the reason that the Bell numbers appear.
Paul
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