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 A067327 #5 Mar 31 2012 13:20:07 %S A067327 1,1,3,4,12,12,28,84,96,48,256,768,912,576,192,2704,8112,9792,6720, %T A067327 3072,768,31168,93504,113856,81408,42240,15360,3072,380608,1141824, %U A067327 1397760,1023744,568320,242688,73728 %N A067327 Triangle related to generalized Catalan numbers A064340. %C A067327 The row polynomials Z(2,2; n,y)= sum(a(n,m)*y^m,m=0..n) appear in c(2,2; x) (the g.f. of C(2,2; n) := A064340(n)) with the first (n+1) expansion terms subtracted, as follows: c(2,2; x)-sum(C(2,2; k)*x^k,k=0..n) = x^(n+1)*G(2,2; x)*Z(2,2; n,y), n>=0, where y=c(4*x) and c(x) is the g.f. of A000108 (Catalan) and G(2,2; x) is the g.f. of C(2,2; n+1), that is G(2,2; x)= (c(2,2; x)-1)/x. Hence G(2,2; x)*Z(2,2; k,c(4*x)) is, for k=0,1,..., the g.f. for C(2,2; n+k), n>=0. %C A067327 Column sequences are: A064340(n), 3*A064340(n+1), Main diagonal gives A002001(n). Row sums give C(2,2; n+1)= A064340(n+1). %F A067327 a(n, 0)= C(2, 2; n) := A064340(n), n>=0; a(n, 1)= 3*C(2, 2; n), n>=1; a(n, m)=4*sum(a(n-1, k), k=(m-1)..(n-1)) if n>=m>=2, else 0. %Y A067327 Cf. A067328 (scaled triangle with 1's in main diagonal). %K A067327 nonn,easy,tabl %O A067327 0,3 %A A067327 _Wolfdieter Lang_, Feb 05 2002