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

0,4

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

Table of n, a(n) for n=0..25.

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

Formula

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

Mathematica

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

Crossrefs

Cf. A260464.

Sequence in context: A299300 A047907 A328420 * A212417 A145874 A147681

Adjacent sequences: A336009 A336010 A336011 * A336013 A336014 A336015

Keyword

nonn

Author

Geoffrey Critzer, Jul 04 2020

Status

approved