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A135081 Column 0 of triangle A135080.

%I A135081 #7 Mar 30 2012 18:37:07
%S A135081 1,1,2,8,50,436,4912,68098,1122952,21488640,468331252,11456367820,
%T A135081 310888085872,9269621420284,301268634277760,10601062978739338,
%U A135081 401550210033474420,16291237867482727084,704847239600911931248
%N A135081 Column 0 of triangle A135080.
%C A135081 Triangle A135080 transforms diagonals in the table of coefficients of successive iterations of x+x^2 (cf. A122888).
%C A135081 Triangle A187005 is defined by: A187005(n,k) = [y^k] R_{n-1}(y+y^2) for k=1..n where R_n(y) is the n-th row polynomial for n>1 with R_1(y)=y.
%H A135081 Paul D. Hanna, <a href="/A135081/b135081.txt">Table of n, a(n) for n=0..50</a>
%F A135081 Equals the main diagonal of triangle A187005.
%o A135081 (PARI) /* As column 0 of triangle A135080 (slower): */
%o A135081 {a(n)=local(F=x,M,N,P); M=matrix(n+2,n+2,r,c,F=x;for(i=1,r+c-2,F=subst(F,x,x+x^2+x*O(x^(n+2))));polcoeff(F,c)); N=matrix(n+1,n+1,r,c,M[r,c]);P=matrix(n+1,n+1,r,c,M[r+1,c]);(P~*N~^-1)[n+1,1]}
%o A135081 (PARI) /* As the main diagonal of triangle A187005 (faster): */
%o A135081 {a(n)=local(Rn=y); for(m=1, n+1, Rn=subst(truncate(Rn), y, y+y^2+y*O(y^m))); polcoeff(Rn/y, n, y)}
%Y A135081 Cf. A135080 (triangle); other columns: A135082, A135083.
%Y A135081 Cf. A187005, A187006, A187007, A187008, A187009.
%K A135081 nonn
%O A135081 0,3
%A A135081 _Paul D. Hanna_, Nov 18 2007