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 A192481 #34 Jun 19 2021 11:06:21
%S A192481 1,1,6,29,162,978,6156,40061,267338,1819238,12576692,88079378,
%T A192481 623581332,4455663876,32090099352,232711721757,1697799727066,
%U A192481 12452943237342,91774314536100,679234371006982,5046438870909244,37623611703611452,281391143518722728
%N A192481 a(n) = Sum_{i=1..n-1} (2^i*C(i)-a(i)) * (2^(n-i)*C(n-i)-a(n-i)), a(1)=1, where C(i)=A000108(i-1) are Catalan numbers.
%C A192481 a(n) is the number of rows with the value false in the truth tables of all bracketed m-implication, case (i), with n distinct variables.
%H A192481 G. C. Greubel, <a href="/A192481/b192481.txt">Table of n, a(n) for n = 1..1000</a>
%H A192481 Volkan Yildiz, <a href="http://arxiv.org/abs/1203.4645">Counting false entries in truth tables of bracketed formulas connected by m-implication</a>, arXiv:1203.4645 [math.CO], 2012.
%H A192481 Volkan Yildiz, <a href="http://arxiv.org/abs/1205.5595">General combinatorical structure of truth tables of bracketed formulas connected by implication</a>, arXiv:1205.5595 [math.CO], 2012.
%F A192481 G.f.: (2 - sqrt(1-8*x) - sqrt(3 - 4*x - 2*sqrt(1-8*x)))/2.
%F A192481 For large n, a(n) is asymptotically (1-2/sqrt 10) * 2^(3n-2)/ sqrt(pi*n^3).
%F A192481 D-finite with recurrence 10*n*(n-1)*(n-2)*a(n) -(n-1)*(n-2)*(149*n-396)*a(n-1) +2*(n-2)*(244*n^2-1618*n+2517)*a(n-2) +4
%F A192481 *(76*n^3-696*n^2+2165*n-2289)*a(n-3) +16*(2*n-9)*(56*n^2-336*n+451)*a(n-4) -256*(n-5)*(2*n-9)*(2*n-11)*a(n-5)=0. - _R. J. Mathar_, Jun 19 2021
%p A192481 C := proc(n) binomial(2*n,n)/(n+1) ; end proc:
%p A192481 A192481 := proc(n) option remember; if n<=1 then n; else add( (2^i*C(i-1)-procname(i))*(2^(n-i)*C(n-i-1)-procname(n-i)), i=1..n-1) ; end if; end proc:
%t A192481 CoefficientList[Series[(2 - Sqrt[1 - 8*x] - Sqrt[3 - 4*x - 2*Sqrt[1 - 8*x]])/2, {x,0,50}], x] (* _G. C. Greubel_, Feb 12 2017 *)
%o A192481 (PARI) x='x+O('x^50); Vec((2-sqrt(1-8*x)-sqrt(3-4*x-2*sqrt(1-8*x)))/2) \\ _G. C. Greubel_, Feb 12 2017
%Y A192481 Cf. A000108, A186997, A192479.
%K A192481 nonn
%O A192481 1,3
%A A192481 _Volkan Yildiz_, Jul 01 2011
%E A192481 a(0) removed from definition by _Georg Fischer_, Jun 19 2021