A228841 E.g.f.: sec(sec(x)-1) (even-indexed coefficients only).

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

Alois P. Heinz, Table of n, a(n) for n = 0..200

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

Cf. A219613, A080832, A003718.

Sequence in context: A136328 A003690 A230143 * A361537 A249938 A195263

Adjacent sequences: A228838 A228839 A228840 * A228842 A228843 A228844

Keyword

nonn

Author

Geoffrey Critzer, Nov 10 2013

Status

approved