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

0,3

Links

Table of n, a(n) for n=0..23.

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

Example

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}}.

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]

Prog

(PARI) 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

Crossrefs

Cf. A007047, A260504.

Sequence in context: A148750 A081562 A216174 * A346658 A246313 A003083

Adjacent sequences: A260461 A260462 A260463 * A260465 A260466 A260467

Keyword

nonn

Author

Geoffrey Critzer, Jul 26 2015

Status

approved