%I A049027
%S A049027 1,1,4,17,74,326,1446,6441,28770,128750,576944,2587850,11615932,52167688,
%T A049027 234383146,1053386937,4735393794,21291593238,95747347176,430624242942,
%U A049027 1936925461644,8712882517188,39195738193836,176335080590442
%N A049027 G.f.: (1-2*x*C)/(1-3*x*C) where C = (1/2-1/2*(1-4*x)^(1/2))/x = g.f. 
               for Catalan numbers A000108.
%C A049027 [a(n+1)] = [1,4,17,74,326,...] is the binomial transform of A059738. 
               [From Philippe DELEHAM (kolotoko(AT)wanadoo.fr), Nov 26 2009]
%H A049027 W. Lang, <a href="http://www.cs.uwaterloo.ca/journals/JIS/index.html">
               On generalizations of Stirling number triangles</a>, J. Integer Seqs., 
               Vol. 3 (2000), #00.2.4.
%H A049027 J. W. Layman, <a href="http://www.cs.uwaterloo.ca/journals/JIS/index.html">
               The Hankel Transform and Some of its Properties</a>, J. Integer Sequences, 
               4 (2001), #01.1.5.
%F A049027 G.f.: x*c(x)/(1-3*x*c(x)), c(x)= g.f. of Catalan numbers A000108.
%F A049027 a(n+1)=sum{k=0..n, 2^k*comb(2n+1, n-k)2(k+1)/(n+k+2)} - Paul Barry (pbarry(AT)wit.ie), 
               Jun 22 2004
%F A049027 a(n) = (9*a(n-1)-Catalan(n-1))/2, n>1. - Vladeta Jovovic (vladeta(AT)eunet.rs), 
               Aug 08 2004
%F A049027 a(n+1)=Sum_{k, 0<=k<=n}A039598(n,k)*2^k . - Philippe DELEHAM (kolotoko(AT)wanadoo.fr), 
               Mar 21 2007
%F A049027 G.f.: 2/ (3 -1/sqrt(1 -4*x)) . - Michael Somos Apr 08 2007
%F A049027 a(n)=Sum_{k, 0<=k<=n}A039599(n,k)*A001045(k), for n>=1 . - Philippe DELEHAM 
               (kolotoko(AT)wanadoo.fr), Jun 10 2007
%o A049027 (PARI) {a(n)= if(n<1, n==0, polcoeff( serreverse( x*(1 +2*x)/ (1 +3*x)^2 
               +x*O(x^n) ), n))} /* Michael Somos Apr 08 2007 */
%o A049027 (PARI) {a(n)= if(n<0, 0, polcoeff( 2/ (3 -1/sqrt(1 -4*x +x*O(x^n))), 
               n))} /* Michael Somos Apr 08 2007 */
%Y A049027 Row sums of triangle A035324. Cf. A000108, A001700.
%Y A049027 Sequence in context: A095940 A125586 A086351 this_sequence A026751 A081568 
               A026378
%Y A049027 Adjacent sequences: A049024 A049025 A049026 this_sequence A049028 A049029 
               A049030
%K A049027 easy,nonn,new
%O A049027 0,3
%A A049027 Wolfdieter Lang (wolfdieter.lang(AT)physik.uni-karlsruhe.de)