Year-end appeal: Please make a donation to the OEIS Foundation to support ongoing development and maintenance of the OEIS. We are now in our 61st year, we have over 378,000 sequences, and we’ve reached 11,000 citations (which often say “discovered thanks to the OEIS”).
%I #4 Jun 20 2015 16:58:26
%S 1,1,3,5,19,42,174,429,1859,4862,21658,58786,266798,742900,3417340,
%T 9694845,45052515,129644790,607283490,1767263190,8331383610,
%U 24466267020,115948830660,343059613650,1632963760974,4861946401452
%N The matrix-vector product A133566 * A000108.
%C A133602 is a companion sequence.
%F 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 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 2*n-3)*(2*n-5)*a(n-2)=0. - _R. J. Mathar_, Jun 20 2015
%e a(5) = C(5) = 42.
%e a(6) = 174 = C(6) + C(5) = 132 + 42.
%p A133603 := proc(n)
%p add(A133566(n+1,k+1)*A000108(k),k=0..n) ;
%p end proc: # _R. J. Mathar_, Jun 20 2015
%Y Cf. A133566, A000108, A133602, A024492 (bisection).
%K nonn,easy
%O 0,3
%A _Gary W. Adamson_, Sep 18 2007