A336012 a(n) is the number of chains from {} to a top element in the poset of even sized subsets of {1,2,...,n} ordered by inclusion.

1, 1, 1, 3, 7, 35, 121, 847, 3907, 35163, 202741, 2230151, 15430207, 200592691, 1619195761, 24287936415, 224061282907, 3809041809419, 39531606447181, 751100522496439, 8661323866026007, 181887801186546147, 2307185279184885001, 53065261421252355023, 734307168916191403507, 18357679222904785087675

Offset: 0

Author

Geoffrey Critzer, Jul 04 2020

Keywords

• nonn

Comments

Note that when n is even there is one top element, namely {1,2,...,n}. When n is odd there are C(n,n-1) = n top elements in the poset.

Links

• Philippe Flajolet and Robert Sedgewick, Analytic Combinatorics, Cambridge Univ. Press, 2009, page 179.

Crossrefs

Cf. A260464.

Programs

Mathematica

nn = 25; Range[0, nn]! CoefficientList[Series[1/(2 - Cosh[z])*(1 + z), {z, 0, nn}], z]

Formula

E.g.f.: 1/(2-cosh(x))*(1+x).