%I A143019
%S A143019 1,1,6,1,7,30,1,8,38,140,1,9,47,187,630,1,10,57,244,874,2772,1,11,68,
%T A143019 312,1186,3958,12012,1,12,80,392,1578,5536,17548,51480,1,13,93,485,2063,
%U A143019 7599,25147,76627,218790,1,14,107,592,2655,10254,35401,112028,330818
%N A143019 Infinite square array read by antidiagonals: a(q,n)=is the coefficient 
               of z^n in the series expansion of C(z)^q/(1-4z)^(3/2), where C(z)=[1-sqrt(1-4z)]/
               (2z) is the Catalan function (q,n=0,1,2,...).
%C A143019 a(q,n)=a(q-1,n)+a(q+1,n-1).
%C A143019 Row 0 is A002457; row 1 is A000531; row 2 is A029760; row 3 is A045720.
%F A143019 a(q,n)=Sum(4^i*binom(2n-2i+q,n-i), i=0..n).
%e A143019 Array starts:
%e A143019 1 6 30 140 630 ...
%e A143019 1 7 38 187 874 ...
%e A143019 1 8 47 244 1186 ...
%e A143019 1 9 57 312 1578 ...
%e A143019 .......
%e A143019 .......
%p A143019 a:=proc(q,n) options operator, arrow: sum(4^i*binomial(2*n-2*i+q, n-i), 
               i= 0.. n) end proc: aa:=proc(q,n) options operator, arrow: a(q-1,
               n-1) end proc: matrix(10,10,aa); # yields sequence in matrix form
%Y A143019 Cf. A002457, A000531, A029760, A045720.
%Y A143019 Sequence in context: A110942 A082830 A046902 this_sequence A156921 A094214 
               A001622
%Y A143019 Adjacent sequences: A143016 A143017 A143018 this_sequence A143020 A143021 
               A143022
%K A143019 nonn
%O A143019 0,3
%A A143019 Emeric Deutsch (deutsch(AT)duke.poly.edu), Jul 24 2008