%I A065096
%S A065096 0,1,6,31,156,785,3978,20335,104856,545073,2854350,15046383,79787700,
%T A065096 425360481,2278586898,12259138975,66216193968,358941938849,
%U A065096 1952111592342,10648449309823,58245727453260,319406931168241,1755674399021466,
               9671384910586511,53384080026230856,295225111836281425,1635532359053982558,
               9075703373174900943,50439671788908739428,280733665349833191873,1564624146618843908130,
               8731422123788687832639
%N A065096 Sums of lists produced by a variant of the iteration that produces the 
               Catalan numbers: start with 0 and at each iteration replace each 
               integer k by the list 0,1,...,k-1,k,k+1,k,k-1,...,1,0 and let a(n) 
               be the sum of the resulting (flattened) list after n iterations.
%C A065096 Number of diagonals emanating from a fixed vertex of a convex (n+3)-gon 
               in all of its dissections. Example: a(1)=1 because in the three dissections 
               of a convex quadrilateral ABCD (namely: empty, {AC}, {BD}) there 
               is only one diagonal emanating from A.
%F A065096 G.f.=(1-3z-sqrt(1-6z+z^2))^2/(16z^3).
%F A065096 a(n)=(1/pi)*Int(x^n*sqrt(-x^2+6x-1)*(x-3)/8,x,3-2sqrt(2),3+2sqrt(2)); 
               - Paul Barry (pbarry(AT)wit.ie), Sep 16 2006
%F A065096 a(0) = 0 and, for n>0, a(n) = Sum_{k=1..n} A001003(k)*A001003(n+1-k) 
               . - DELEHAM Philippe (kolotoko(AT)wanadoo.fr), Jan 27 2004
%t A065096 Table[Plus@@Flatten[Nest[ #/.a_Integer:> Join[Range[0, a+1], Range[a, 
               0, -1]]&, {0}, n]], {n, 0, 10}]
%t A065096 Table[Range[n, 0, -1].Table[a[n, k], {k, 0, n}], {n, 0, 36}] with a[n, 
               k] as defined in A033877.
%Y A065096 Cf. A000108, A001003.
%Y A065096 Sequence in context: A026705 A003463 A026771 this_sequence A077352 A038223 
               A022034
%Y A065096 Adjacent sequences: A065093 A065094 A065095 this_sequence A065097 A065098 
               A065099
%K A065096 nonn
%O A065096 0,3
%A A065096 Wouter Meeussen (wouter.meeussen(AT)pandora.be), Nov 11 2001