

A104345


Triangle read by rows: T(n,k) is the number of alternating permutations on [n+1] with 1 in position k+1, 0<=k<=n.


1



1, 1, 1, 1, 2, 1, 2, 3, 3, 2, 5, 8, 6, 8, 5, 16, 25, 20, 20, 25, 16, 61, 96, 75, 80, 75, 96, 61, 272, 427, 336, 350, 350, 336, 427, 272, 1385, 2176, 1708, 1792, 1750, 1792, 1708, 2176, 1385, 7936, 12465, 9792, 10248, 10080, 10080, 10248, 9792, 12465, 7936
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OFFSET

0,5


LINKS

Table of n, a(n) for n=0..54.


FORMULA

The mixed ogf/egf is Sum[T(n, k)*x^n/n!*y^k, {n>=k>=0}] = (sec(x) + tan(x))*(sec(x*y) + tan(x*y)).


EXAMPLE

Table begins
\ k..0....1....2....3....4....
n
0 ..1
1 ..1....1
2 ..1....2....1
3 ..2....3....3....2
4 ..5....8....6....8....5
5 .16...25...20...20...25...16
6 .61...96...75...80...75...96...61
7 272..427..336..350..350..336..427..272
For example, a(3,1) counts 2143, 3142, 4132the alternating permutations on [4] with 1 in position 2.


CROSSREFS

Cf. A104346. Row sums are A001250; column k=0 and main diagonal are the updown numbers (A000111); column k=1 is A065619.
Sequence in context: A024376 A230128 A123265 * A244516 A002339 A123243
Adjacent sequences: A104342 A104343 A104344 * A104346 A104347 A104348


KEYWORD

nonn,tabl


AUTHOR

David Callan, Mar 02 2005


STATUS

approved



