cp's OEIS Frontend

A181472 Riordan array ((1+x)/(1+2x+2x^2),x(1+x)/(1+2x+2x^2)).

%I A181472 #13 Aug 12 2015 14:34:28
%S A181472 1,-1,1,0,-2,1,2,1,-3,1,-4,4,3,-4,1,4,-12,5,6,-5,1,0,16,-24,4,10,-6,1,
%T A181472 -8,-4,42,-39,0,15,-7,1,16,-32,-24,88,-55,-8,21,-8,1,-16,80,-72,-80,
%U A181472 159,-69,-21,28,-9,1,0,-96,240,-112,-200,258,-77,-40,36,-10,1
%N A181472 Riordan array ((1+x)/(1+2x+2x^2),x(1+x)/(1+2x+2x^2)).
%C A181472 Inverse is A054336. Coefficient array for Faber polynomials (of second kind) defined by f(x)=x+1-sum{(-1)^k/x^k,k>=1}.
%C A181472 Subtriangle of the triangle given by (0, -1, 1, -2, 0, 0, 0, 0, 0, 0, 0, ...) DELTA (1, 0, 0, 0, 0, 0, 0, 0, ...) where DELTA is the operator defined in A084938. -_Philippe Deléham_, Feb 20 2013
%F A181472 T(n,m)=sum(k=m..m,(-2)^(k-m)*binomial(k,n-k)*binomial(k-1,m-1)), n,m>0, [From Vladimir Kruchinin, Mar 09 2011]
%F A181472 T(n,k) = T(n-1,k-1) + T(n-2,k-1) -2*T(n-1,k) - 2*T(n-2,k), T(0,0) = T(1,1) = 1, T(1,0) = -1, T(n,k) = 0 if k<0 or if k>n. -_Philippe Deléham_, Feb 20 2013
%F A181472 G.f.: (-1-x)/(-1-2*x-2*x^2+x*y+x^2*y). - _R. J. Mathar_, Aug 12 2015
%e A181472 Triangle begins
%e A181472 1,
%e A181472 -1, 1,
%e A181472 0, -2, 1,
%e A181472 2, 1, -3, 1,
%e A181472 -4, 4, 3, -4, 1,
%e A181472 4, -12, 5, 6, -5, 1,
%e A181472 0, 16, -24, 4, 10, -6, 1,
%e A181472 -8, -4, 42, -39, 0, 15, -7, 1,
%e A181472 16, -32, -24, 88, -55, -8, 21, -8, 1
%e A181472 Production matrix is
%e A181472 -1, 1,
%e A181472 -1, -1, 1,
%e A181472 0, -1, -1, 1,
%e A181472 -1, 0, -1, -1, 1,
%e A181472 0, -1, 0, -1, -1, 1,
%e A181472 -2, 0, -1, 0, -1, -1, 1,
%e A181472 0, -2, 0, -1, 0, -1, -1, 1,
%e A181472 -5, 0, -2, 0, -1, 0, -1, -1, 1,
%e A181472 0, -5, 0, -2, 0, -1, 0, -1, -1, 1
%e A181472 -14, 0, -5, 0, -2, 0, -1, 0, -1, -1, 1
%e A181472 based on the aerated Catalan numbers.
%e A181472 Triangle (0, -1, 1, -2, 0, 0, 0, ...) DELTA (1, 0, 0, 0, ...) begins:
%e A181472 1
%e A181472 0, 1
%e A181472 0, -1, 1
%e A181472 0, 0, -2, 1
%e A181472 0, 2, 1, -3, 1
%e A181472 0, -4, 4, 3, -4, 1
%e A181472 0, 4, -12, 5, 6, -5, 1. -_Philippe Deléham_, Feb 20 2013
%K A181472 easy,sign,tabl
%O A181472 0,5
%A A181472 _Paul Barry_, Oct 21 2010