Search: id:A030238
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%I A030238
%S A030238 1,1,3,7,20,59,184,593,1964,6642,22845,79667,281037,1001092,
%T A030238 3595865,13009673,47366251,173415176,638044203,2357941142,
%U A030238 8748646386,32576869203,121701491701,456012458965,1713339737086
%N A030238 Backwards shallow diagonal sums of Catalan triangle A009766.
%C A030238 Number of linear forests of planted planar trees with n nodes (Christian 
               G. Bower).
%C A030238 Number of ordered trees with n+2 edges and having no branches of length 
               1 starting from the root. Example: a(1)=1 because the only ordered 
               tree with 3 edges having no branch of length 1 starting from the 
               root is the path tree of length 3. a(n)=A127158(n+2,0). - Emeric 
               Deutsch (deutsch(AT)duke.poly.edu), Mar 01 2007
%C A030238 Hankel transform is A056520. - Paul Barry (pbarry(AT)wit.ie), Oct 16 
               2007
%F A030238 INVERT transform of 1, 2, 2, 5, 14, 42, 132... (cf. A000108).
%F A030238 a(n)=sum{k=0..floor(n/2), (k+1)binomial(2n-3k+1, n-k+1)/(2n-3k+1)}. Diagonal 
               sums of A033184. - Paul Barry (pbarry(AT)wit.ie), Jun 22 2004
%F A030238 a(n)=sum{k=0..floor(n/2), (k+1)binomial(2n-3k, n-k)/(n-k+1)} - Paul Barry 
               (pbarry(AT)wit.ie), Feb 02 2005
%F A030238 G.f.=[1-sqrt(1-4z)]/[z(2-z+z*sqrt(1-4z)]. - Emeric Deutsch (deutsch(AT)duke.poly.edu), 
               Mar 01 2007
%p A030238 g:=(1-sqrt(1-4*z))/z/(2-z+z*sqrt(1-4*z)): gser:=series(g,z=0,30): seq(coeff(gser,
               z,n),n=0..25); - Emeric Deutsch (deutsch(AT)duke.poly.edu), Mar 01 
               2007
%t A030238 Sum[ triangle[ n-k, (n-k)-(k-1) ], {k, 1, Floor[ (n+1)/2 ]} ]
%Y A030238 Cf. A127158.
%Y A030238 Sequence in context: A129429 A084204 A132364 this_sequence A110490 A132868 
               A056783
%Y A030238 Adjacent sequences: A030235 A030236 A030237 this_sequence A030239 A030240 
               A030241
%K A030238 nonn
%O A030238 0,3
%A A030238 Wouter Meeussen (wouter.meeussen(AT)pandora.be)
%E A030238 More terms from Christian G. Bower (bowerc(AT)usa.net), Apr 15 1998.

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