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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 (list; table; graph; refs; listen; history; text; internal format)
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, 4132---the alternating permutations on [4] with 1 in position 2.

CROSSREFS

Cf. A104346. Row sums are A001250; column k=0 and main diagonal are the up-down 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

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Last modified September 20 12:42 EDT 2017. Contains 292271 sequences.