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A228841
E.g.f.: sec(sec(x)-1) (even-indexed coefficients only).
1
1, 0, 3, 75, 3108, 205125, 19839633, 2643131400, 463873573803, 103710628476075, 28775903316814668, 9702563010998171325, 3907429085273025561153, 1852516229654506870381200, 1021325008815288529961197683, 647900078249178232882473232875
OFFSET
0,3
COMMENTS
Call a zig permutation a permutation p(1),p(2),...,p(2n) such that p(1)>p(2)< ... > p(2n) Cf. A000364. Consider the set of all set partitions of {1,2,...,2n} into an even number of even sized blocks. a(n) is the number of ways to build a zig permutation on each block and then build a zig permutation on the set formed from a representative (say the smallest element) of each block.
LINKS
EXAMPLE
a(3) = 75. There are 15 set partitions of {1,2,3,4,5,6} that have an even number of even sized blocks Cf. A059386. They all have the same structure: 2/4. We build a zig permutation on each block in 1*5=5 ways. For each of these we then build a zig permutation on a representative from each of the 2 blocks in 1 way. So 5*1=5 and there are 15 such partitions so 5 *15 =75.
MATHEMATICA
nn=30; Insert[Select[Range[0, nn]!CoefficientList[Series[Sec[Sec[x]-1], {x, 0, nn}], x], #>0&], 0, 2]
CROSSREFS
KEYWORD
nonn
AUTHOR
Geoffrey Critzer, Nov 10 2013
STATUS
approved