Search: id:A127632
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%I A127632
%S A127632 1,1,3,11,44,185,804,3579,16229,74690,347984,1638169,7780876,37245028,
%T A127632 179503340,870374211,4243141332,20786340271,102275718924,505235129250,
%U A127632 2504876652190,12459922302900,62167152967680,311040862133625
%N A127632 Expansion of 1/(1 - x*c(x) * c(x*c(x))), where c(x) is the g.f. of A000108.
%C A127632 Row sums of number triangle A127631. Hankel transform appears to be A075845.
%C A127632 Catalan transform of Catalan numbers . - Philippe DELEHAM (kolotoko(AT)wanadoo.fr), 
               Jun 20 2007
%F A127632 a(n) = A127714(n+1,2n+1).
%F A127632 G.f. A(x) satisfies 0 = 1 - A(x) + A(x)^2 * x * c(x) where c(x) is the 
               g.f. of A000108.
%F A127632 G.f.: 2/(1 + sqrt( 2 * sqrt(1 -4*x) - 1)). - Michael Somos May 04 2007
%F A127632 a(n)=Sum_{k, 0<=k<=n}A106566(n,k)*A000108(k). - Philippe DELEHAM (kolotoko(AT)wanadoo.fr), 
               Jun 20 2007
%o A127632 (PARI) {a(n)= if(n<1, n==0, polcoeff( serreverse( x*(1-x)^3*(1-x^3)/(1-x^2)^4 
               +x*O(x^n) ), n))} /* Michael Somos May 04 2007 */
%o A127632 (PARI) {a(n)= local(A); if(n<1, n==0, A= serreverse( x-x^2 +x*O(x^n) 
               ); polcoeff( 1/(1 - subst(A, x, A)), n))} /* Michael Somos May 04 
               2007 */
%Y A127632 Cf. A127714.
%Y A127632 Sequence in context: A132840 A091200 A151105 this_sequence A061706 A167012 
               A167013
%Y A127632 Adjacent sequences: A127629 A127630 A127631 this_sequence A127633 A127634 
               A127635
%K A127632 easy,nonn
%O A127632 0,3
%A A127632 Paul Barry (pbarry(AT)wit.ie), Jan 20 2007, Jan 25 2007

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