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A117270 Matrix log of triangle M = A117269, which satisfies: M - (M-I)^2 = C where C is Pascal's triangle.

%I A117270 #4 Mar 30 2012 18:36:56
%S A117270 0,1,0,2,2,0,12,6,3,0,134,48,12,4,0,2100,670,120,20,5,0,42302,12600,
%T A117270 2010,240,30,6,0,1041852,296114,44100,4690,420,42,7,0,30331814,
%U A117270 8334816,1184456,117600,9380,672,56,8,0,1019056260,272986326,37506672,3553368
%N A117270 Matrix log of triangle M = A117269, which satisfies: M - (M-I)^2 = C where C is Pascal's triangle.
%C A117270 E.g.f. of column 0 (A117271) is log( (3-sqrt(5-4*exp(x)))/2 ) and equals the log of the g.f. of column 0 of A117269.
%F A117270 T(n,k) = A117271(n-k)*C(n,k).
%e A117270 Triangle begins:
%e A117270 0;
%e A117270 1,0;
%e A117270 2,2,0;
%e A117270 12,6,3,0;
%e A117270 134,48,12,4,0;
%e A117270 2100,670,120,20,5,0;
%e A117270 42302,12600,2010,240,30,6,0;
%e A117270 1041852,296114,44100,4690,420,42,7,0; ...
%o A117270 (PARI) {a(n)=local(C=matrix(n+1,n+1,r,c,if(r>=c,binomial(r-1,c-1))),M=C,L); for(i=1,n+1,M=(M-M^0)^2+C);L=sum(r=1,#M,-(M^0-M)^r/r);return(L[n+1,1])}
%Y A117270 Cf. A117269, A117271 (column 0).
%K A117270 nonn,tabl
%O A117270 0,4
%A A117270 _Paul D. Hanna_, Mar 05 2006