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

%I #4 Mar 30 2012 18:36:56

%S 0,1,0,2,2,0,12,6,3,0,134,48,12,4,0,2100,670,120,20,5,0,42302,12600,

%T 2010,240,30,6,0,1041852,296114,44100,4690,420,42,7,0,30331814,

%U 8334816,1184456,117600,9380,672,56,8,0,1019056260,272986326,37506672,3553368

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

%C 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 T(n,k) = A117271(n-k)*C(n,k).

%e Triangle begins:

%e 0;

%e 1,0;

%e 2,2,0;

%e 12,6,3,0;

%e 134,48,12,4,0;

%e 2100,670,120,20,5,0;

%e 42302,12600,2010,240,30,6,0;

%e 1041852,296114,44100,4690,420,42,7,0; ...

%o (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 Cf. A117269, A117271 (column 0).

%K nonn,tabl

%O 0,4

%A _Paul D. Hanna_, Mar 05 2006

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Last modified December 5 09:29 EST 2023. Contains 367589 sequences. (Running on oeis4.)