[seqfan] Catalan-related sequences with floretions

[Creighton Kenneth Dement]

Here's one more case that I find interesting:

1diaKtesseq: [1, 0, 1, 0, 2, 0, 5, 0, 14, 0] Catalan
2diaKtesposseq: [2, 1, 4, 7, 24, 66, 222, 715, 2452, 8398] unlisted
2diaKtesnegseq: [0, -1, -2, -7, -20, -66, -212, -715, -2424, -8398] A000150


1emKseq: [1, 0, 1, 0, 2, 0, 5, 0, 14, 0] Catalan
1emKposseq: [1, 1, 3, 7, 22, 66, 217, 715, 2438, 8398] A007595
1emKnegseq: [0, -1, -2, -7, -20, -66, -212, -715, -2424, -8398] A000150


1emIseq: [1, 0, 1, 0, 2, 0, 5, 0, 14, 0] Catalan
1emIposseq: [1, 2, 3, 10, 22, 76, 217, 750, 2438, 8524] A089880
1emInegseq: [0, -2, -2, -10, -20, -76, -212, -750, -2424, -8524] unlisted

You'll notice that for each sequence triplet, the first one is
always (1, 0, 1, 0, 2, 0, 5, 0, 14, 0, ...) and it is the sum of the other
two (with the first triplet it is necessary to divide all terms by 2).

If I have to I will, but I would much rather someone else submit the two
unlisted sequences with a deeper knowledge of Catalan numbers than myself.
There is no need to reference floretions...

Sincerely,
Creighton