A260464 Number of chains in the poset of even-sized subsets of {1,2,...,n} ordered by inclusion.
1, 1, 3, 7, 27, 91, 483, 2227, 15627, 92491, 810963, 5866147, 61720827, 527635291, 6476783043, 63886537267, 896245131627, 10019232896491, 158126425788723, 1975680877259587, 34645295464104027, 478434297205284091, 9228741116739540003, 139581878985127217107
Offset: 0
Keywords
Examples
a(3)=7 because there are 4 chains of length zero: {{}}; {{1,2}}; {{1,3}}; {{2,3}} and there are 3 chains of length one: {{},{1,2}}; {{},{1,3}}; {{},{2,3}}.
Programs
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Mathematica
nn = 20; c = Cosh[x] - 1; s = Sinh[x];Range[0, nn]! CoefficientList[Series[(c^2 + 2 c + 1 + s c + s)/(1 - c), {x, 0, nn}], x] -
PARI
my(x='x+O('x^33), c = cosh(x)-1, s=sinh(x)); Vec(serlaplace( (c^2 + 2*c + 1 + s*c + s)/(1 - c) )) \\ Joerg Arndt, Jul 27 2015
Formula
E.g.f.: (c^2 + 2*c + 1 + s*c + s)/(1 - c) where c = cosh(x)-1 and s=sinh(x).
a(n) ~ n! * (4/sqrt(3)+2 + (4/sqrt(3)-2)*(-1)^n) / log(2+sqrt(3))^(n+1). - Vaclav Kotesovec, Jul 27 2015