%I A086616
%S A086616 1,3,9,31,121,515,2321,10879,52465,258563,1296281,6589727,33887465,
%T A086616 175966211,921353249,4858956287,25786112993,137604139011,737922992937,
%U A086616 3974647310111,21493266631001,116642921832963,635074797251889
%N A086616 Row sums of triangle A086614.
%C A086616 Partial sums of the sequence of the large Schroeder numbers (A006318). 
               - Emeric Deutsch (deutsch(AT)duke.poly.edu), Dec 20 2004
%C A086616 Hankel transform is A136577(n+1). [From Paul Barry (pbarry(AT)wit.ie), 
               Jun 03 2009]
%F A086616 G.f.: A(x) = 1/(1-x)^2 + x*A(x)^2.
%F A086616 a(1)=1, a(n)=n+sum(i=1, n-1, a(i)*a(n-i)). - Benoit Cloitre (benoit7848c(AT)orange.fr), 
               Mar 16 2004
%F A086616 G.f.: [1-x-sqrt(1-6x+x^2)]/[2x(1-x)]. Cf. A001003. - R. Stephan, Mar 
               23 2004
%F A086616 a(n)=sum{k=0..n, C(n+k+1,2k+1)*A000108(k)}. [From Paul Barry (pbarry(AT)wit.ie), 
               Jun 03 2009]
%e A086616 a(1)=2+1=3, a(2)=3+4+2=9, a(3)=4+10+12+5=31, a(4)=5+20+42+40+14=121.
%Y A086616 Cf. A086614 (triangle), A086615 (antidiagonal sums).
%Y A086616 Cf. A006318.
%Y A086616 Sequence in context: A151037 A066571 A087648 this_sequence A040027 A071603 
               A090595
%Y A086616 Adjacent sequences: A086613 A086614 A086615 this_sequence A086617 A086618 
               A086619
%K A086616 nonn
%O A086616 0,2
%A A086616 Paul D. Hanna (pauldhanna(AT)juno.com), Jul 24 2003