%I A136467
%S A136467 1,1,1,1,4,1,4,32,16,1,70,848,576,64,1,4368,75648,62208,9216,256,1,
%T A136467 906192,22313216,21169152,3792896,143360,1024,1,621216192,21827627008,
%U A136467 23212261376,4793434112,223215616,2228224,4096,1,1429702652400
%N A136467 Triangle T, read by rows, where column 0 of T^m equals C(m*2^(n-1), n) 
               as n=0,1,2,3,..., for all m.
%C A136467 Column 0 of T^(n+1) = row n 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 = A136467.
%F A136467 Diagonals: T(n+1,n) = 4^n; T(n+2,n) = (2^(n+1) + n-1)*8^n.
%e A136467 Triangle T begins:
%e A136467 1;
%e A136467 1, 1;
%e A136467 1, 4, 1;
%e A136467 4, 32, 16, 1;
%e A136467 70, 848, 576, 64, 1;
%e A136467 4368, 75648, 62208, 9216, 256, 1;
%e A136467 906192, 22313216, 21169152, 3792896, 143360, 1024, 1;
%e A136467 621216192, 21827627008, 23212261376, 4793434112, 223215616, 2228224, 
               4096, 1;
%e A136467 1429702652400, 71889350288384, 83889221697536, 19373156990976, 1055047811072, 
               13257146368, 34865152, 16384, 1; ...
%e A136467 Column 0 of T^m is given by: [T^m](n,0) = C(m*2^(n-1), n) for n>=0.
%o A136467 (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)[n+1,
               k+1]}
%Y A136467 Cf. columns: A136465, A136468, A136469; A136470 (matrix square); A136462.
%Y A136467 Sequence in context: A143461 A066808 A033918 this_sequence A079188 A076810 
               A061642
%Y A136467 Adjacent sequences: A136464 A136465 A136466 this_sequence A136468 A136469 
               A136470
%K A136467 nonn,tabl
%O A136467 0,5
%A A136467 Paul D. Hanna (pauldhanna(AT)juno.com), Dec 31 2007