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 A133603 #4 Jun 20 2015 16:58:26 %S A133603 1,1,3,5,19,42,174,429,1859,4862,21658,58786,266798,742900,3417340, %T A133603 9694845,45052515,129644790,607283490,1767263190,8331383610, %U A133603 24466267020,115948830660,343059613650,1632963760974,4861946401452 %N A133603 The matrix-vector product A133566 * A000108. %C A133603 A133602 is a companion sequence. %F A133603 A133566 * A000108 where A133566 = an infinite lower triangular matrix and A000108 = the Catalan sequence. For odd n, a(n) = C(n). For even n, a(n) = C(n) + C(n-1) = A005807(n-1). %F A133603 Conjecture: n*(n-2)*(3*n-1)*(n+1)*a(n) -8*n*(2*n-3)*a(n-1) -4*(n-1)*(3*n+2)*( %F A133603 2*n-3)*(2*n-5)*a(n-2)=0. - _R. J. Mathar_, Jun 20 2015 %e A133603 a(5) = C(5) = 42. %e A133603 a(6) = 174 = C(6) + C(5) = 132 + 42. %p A133603 A133603 := proc(n) %p A133603 add(A133566(n+1,k+1)*A000108(k),k=0..n) ; %p A133603 end proc: # _R. J. Mathar_, Jun 20 2015 %Y A133603 Cf. A133566, A000108, A133602, A024492 (bisection). %K A133603 nonn,easy %O A133603 0,3 %A A133603 _Gary W. Adamson_, Sep 18 2007