Search: id:A158843
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%I A158843
%S A158843 1,2,20,952,336112,742166496,10043945021760,814531629739559808,
%T A158843 393150002983518264270592,1123538097532735360702239462912,
%U A158843 18948231465474675384343860006353603584
%N A158843 G.f.: A(x) = exp( Sum_{n>=1} A001333(n)^n * 2^n*x^n/n ).
%C A158843 Compare to g.f.: exp( Sum_{n>=1} 2*A001333(n)*x^n/n ) = 1/(1-2*x-x^2), 
               which is the g.f. of the Pell numbers A000129 (with offset), where 
               A001333(n) = A000129(n+1) - A000129(n).
%e A158843 G.f.: A(x) = 1 + 2*x + 20*x^2 + 952*x^3 + 336112*x^4 + 742166496*x^5 
               +...
%e A158843 log(A(x)) = 2*x + 6^2*x^2/2 + 14^3*x^3/3 + 34^4*x^4/4 + 82^5*x^5/5 +...
%e A158843 log(G(x)) = 2*x + 6*x^2/2 + 14*x^3/3 + 34*x^4/4 + 82*x^5/5 +...
%e A158843 G(x) = 1 + 2*x + 5*x^2 + 12*x^3 + 29*x^4 + 70*x^5 + 169*x^6 +... (A000129).
%o A158843 (PARI) {a(n)=local(LD=Vec(2*(1+x)/(1-2*x-x^2 +x*O(x^n)))); polcoeff(exp(sum(m=1,
               n,LD[m]^m*x^m/m)+x*O(x^n)),n)}
%Y A158843 Cf. A000129, A001333.
%Y A158843 Sequence in context: A013148 A006547 A135757 this_sequence A008793 A015192 
               A012790
%Y A158843 Adjacent sequences: A158840 A158841 A158842 this_sequence A158844 A158845 
               A158846
%K A158843 nonn
%O A158843 0,2
%A A158843 Paul D. Hanna (pauldhanna(AT)juno.com), Apr 09 2009

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