%I A071969
%S A071969 1,1,2,6,19,63,219,787,2897,10869,41414,159822,623391,2453727,9733866,
               38877318,
%T A071969 156206233,630947421,2560537092,10435207116,42689715279,175243923783,721649457417,
%U A071969 2980276087005,12340456995177,51222441676513,213090270498764,888321276659112
%N A071969 Sum( binomial(n+1,k)*binomial(2*n-3*k,n-3*k)/(n+1),k=0..floor(n/3)).
%C A071969 Diagonal of A071946. - Emeric Deutsch (deutsch(AT)duke.poly.edu), Dec 
               15 2004
%D A071969 D. Merlini et al., Underdiagonal lattice paths with unrestricted steps, 
               Discrete Appl. Math., 91 (1999), 197-213 (d_n page 209).
%H A071969 D. Merlini et al., <a href="http://www.dsi.unifi.it/~merlini/under.ps">
               Underdiagonal lattice paths with unrestricted steps</a>, Discrete 
               Appl. Math., 91 (1999), 197-213 (d_n page 209).
%F A071969 G.f. (offset 1) is series reversion of (x-x^2)/(1+x^3).
%p A071969 A071969 := n->add( binomial(n+1,k)*binomial(2*n-3*k,n-3*k)/(n+1),k=0..floor(n/
               3));
%p A071969 Order:=30: g:=solve(series((H-H^2)/(1+H^3),H)=z,H): seq(coeff(g,z^n),
               n=1..28); (Deutsch)
%o A071969 (PARI) a(n)=if(n<0,0,polcoeff(serreverse((x-x^2)/(1+x^3)+x^2*O(x^n)),
               n+1))
%Y A071969 Cf. A071946.
%Y A071969 Sequence in context: A001170 A001168 A119255 this_sequence A063030 A148467 
               A148468
%Y A071969 Adjacent sequences: A071966 A071967 A071968 this_sequence A071970 A071971 
               A071972
%K A071969 nonn
%O A071969 0,3
%A A071969 N. J. A. Sloane (njas(AT)research.att.com), Jun 17 2002