This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.
%I A260464 #21 Nov 15 2024 06:58:55
%S A260464 1,1,3,7,27,91,483,2227,15627,92491,810963,5866147,61720827,527635291,
%T A260464 6476783043,63886537267,896245131627,10019232896491,158126425788723,
%U A260464 1975680877259587,34645295464104027,478434297205284091,9228741116739540003,139581878985127217107
%N A260464 Number of chains in the poset of even-sized subsets of {1,2,...,n} ordered by inclusion.
%F A260464 E.g.f.: (c^2 + 2*c + 1 + s*c + s)/(1 - c) where c = cosh(x)-1 and s=sinh(x).
%F A260464 a(n) ~ n! * (4/sqrt(3)+2 + (4/sqrt(3)-2)*(-1)^n) / log(2+sqrt(3))^(n+1). - _Vaclav Kotesovec_, Jul 27 2015
%e A260464 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}}.
%t A260464 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]
%o A260464 (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
%Y A260464 Cf. A007047, A260504.
%K A260464 nonn
%O A260464 0,3
%A A260464 _Geoffrey Critzer_, Jul 26 2015