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A136470 Triangle T, read by rows, where column 0 of T^m = {C(m*2^n, n), n>=0} for all m.

%I A136470 #6 Jan 16 2016 19:52:48
%S A136470 1,2,1,6,8,1,56,128,32,1,1820,6048,2176,128,1,201376,912128,419328,
%T A136470 34816,512,1,74974368,449708544,249300992,26198016,548864,2048,1,
%U A136470 94525795200,739136655360,477013868544,59943682048,1604059136,8650752,8192,1,409663695276000,4132411271661568,3028532448264192,439222754869248,14159357935616,98723430400,136839168,32768,1,6208116950265950720,80121787455478857728,65415571433959456768,10679727629898088448,399723620798038016,3391703461396480,6141702569984,2172649472,131072,1
%N A136470 Triangle T, read by rows, where column 0 of T^m = {C(m*2^n, n), n>=0} for all m.
%C A136470 Column 0 of T^(n+1) = row 2n+1 of square array A136462 defined by: A136462(n,k) = C((n+1)*2^(k-1), k); T^n denotes the n-th matrix power of this triangle T = A136470.
%F A136470 Equals the matrix square of triangle A136467.
%F A136470 Diagonals: T(n+1,n) = 2*4^n; T(n+2,n) = 2*8^n*(2^(n+2) + n-1).
%e A136470 Triangle T begins:
%e A136470 1;
%e A136470 2, 1;
%e A136470 6, 8, 1;
%e A136470 56, 128, 32, 1;
%e A136470 1820, 6048, 2176, 128, 1;
%e A136470 201376, 912128, 419328, 34816, 512, 1;
%e A136470 74974368, 449708544, 249300992, 26198016, 548864, 2048, 1;
%e A136470 94525795200, 739136655360, 477013868544, 59943682048, 1604059136, 8650752, 8192, 1;
%e A136470 409663695276000, 4132411271661568, 3028532448264192, 439222754869248, 14159357935616, 98723430400, 136839168, 32768, 1; ...
%e A136470 Column 0 of T^m is given by: [T^m](n,0) = C(m*2^n, n) for n>=0.
%o A136470 (PARI) {T(n,k)=local(M=matrix(n+1,n+1,r,c,binomial(r*2^(c-2),c-1)),P); P=matrix(n+1,n+1,r,c,binomial((r+1)*2^(c-2),c-1));((P~*M~^-1)^2)[n+1,k+1]}
%o A136470 for(n=0, 10, for(k=0, n, print1(T(n, k), ", ")); print(""))
%Y A136470 Cf. columns: A014070, A136471, A136472; A136467 (matrix square-root); A136462.
%K A136470 nonn,tabl
%O A136470 0,2
%A A136470 _Paul D. Hanna_, Dec 31 2007