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Column 0 of matrix square of triangle A134049; a(n) = [A134049^2](n,0) = A134049(n+1,1)/2^n.
6

%I #5 Jun 22 2016 22:48:28

%S 1,2,10,134,5296,654070,263360560,357003975476,1669795729960304,

%T 27463303283181254246,1611997717693371814854368,

%U 341658984940005114542280763676,263970944698309599873282861747395376,749286382285580603530480750573407791776124,7865298802379026632132665433693770690173266977568,307033171145749412684239046186235780900756052952468535976,44787318088048191911792372704769709799574702261206913048329680992

%N Column 0 of matrix square of triangle A134049; a(n) = [A134049^2](n,0) = A134049(n+1,1)/2^n.

%H Paul D. Hanna, <a href="/A134051/b134051.txt">Table of n, a(n) for n = 0..40</a>

%e Triangle T=A134049 has the following properties:

%e (1) [T^(2^m)](n,k) = T(n+m,k+m)/(2^m)^(n-k) for m>=0; and

%e (2) [T^( 1/2^(n-1) )](n,k) = (2^k)^(n-k) for n>=k>=0.

%o (PARI) {a(n)=local(M=Mat(1),L,R);for(i=1,n+1, L=sum(j=1,#M,-(M^0-M)^j/j);M=sum(j=0,#L,(L/2^(#L-1))^j/j!); R=matrix(#M+1,#M+1,r,c,if(r>=c,if(r<=#M,M[r,c],2^((c-1)*(#M+1-c))))); M=R^(2^(#R-2)) );M[n+2,2]/2^n}

%o for(n=0, 20, print1(a(n), ", "))

%Y Cf. A134049; columns: A134050, A134052, A134053; A134054 (row sums).

%K nonn

%O 0,2

%A _Paul D. Hanna_, Oct 04 2007