Search: id:A027826
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%I A027826
%S A027826 1,1,2,4,9,21,50,120,290,706,1732,4280,10644,26612,66824,168384,
%T A027826 425481,1077529,2733746,6945812,17669149,44994345,114682042,
%U A027826 292544200,746831570,1907983346,4877966628,12479883736,31951158024
%N A027826 Inverse binomial transform of a_0 = 1, a_1, a_2, etc. is a_0, 0, a_1, 
               0, a_2, 0, etc.
%C A027826 The self-convolution equals A051163. - Paul D. Hanna (pauldhanna(AT)juno.com), 
               Nov 23 2004
%C A027826 Equals row sums of triangle A152193. [From Gary W. Adamson (qntmpkt(AT)yahoo.com), 
               Nov 28 2008]
%C A027826 Hankel transform is A166446(n+1). [From Paul Barry (pbarry(AT)wit.ie), 
               Oct 13 2009]
%H A027826 N. J. A. Sloane, <a href="transforms.txt">Transforms</a>
%F A027826 G.f. A(x) satisfies A(x^2)=A(x/(1+x))/(1+x) and A(x)=A(x^2/(1-x)^2)/(1-x).
%F A027826 Contribution from Paul Barry (pbarry(AT)wit.ie), Jul 05 2009: (Start)
%F A027826 G.f.: (1-x)/((1-x)^2-x^2-x^4/((1-x)^2-x^2-x^4/(1-... (continued fraction);
%F A027826 a(n)=sum{k=0..n, C(n,2k)*A001006(k)}. (End)
%F A027826 G.f.: ((1-x)*(1-2x-sqrt((1-2x)^2-4x^4))/(2x^4). [From Paul Barry (pbarry(AT)wit.ie), 
               Oct 13 2009]
%o A027826 (PARI) a(n)=local(A,m); if(n<0,0,m=1; A=1+O(x); while(m<=n,m*=2; A=subst(A,
               x,(x/(1-x))^2)/(1-x)); polcoeff(A,n))
%Y A027826 Cf. A051163.
%Y A027826 A152193 [From Gary W. Adamson (qntmpkt(AT)yahoo.com), Nov 28 2008]
%Y A027826 Sequence in context: A052921 A018905 A024537 this_sequence A091964 A092423 
               A091600
%Y A027826 Adjacent sequences: A027823 A027824 A027825 this_sequence A027827 A027828 
               A027829
%K A027826 nonn
%O A027826 0,3
%A A027826 Allan Wechsler (acw(AT)alum.mit.edu)

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