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%I #7 Jan 19 2019 20:30:59
%S 1,1,1,1,3,1,1,7,7,1,1,15,455,15,1,1,31,4495,4495,31,1,1,63,39711,
%T 553270671,39711,63,1,1,127,333375,89356415775,89356415775,333375,127,
%U 1,1,255,2731135,12801990477375,629921975126394617164575,12801990477375
%N Triangle t(n,m) read by rows: t(n,m) = binomial(2^n-1, 2^m-1) if n >= 2*m, otherwise symmetrically extended t(n,m) = t(n,n-m).
%C Row sums are 1, 2, 5, 16, 487, 9054, 553350221, 178713498556, 629921975151998603582107, 52571341051325843383483521914, ...
%e 1;
%e 1, 1;
%e 1, 3, 1;
%e 1, 7, 7, 1;
%e 1, 15, 455, 15, 1;
%e 1, 31, 4495, 4495, 31, 1;
%e 1, 63, 39711, 553270671, 39711, 63, 1;
%e 1, 127, 333375, 89356415775, 89356415775, 333375, 127, 1;
%e 1, 255, 2731135, 12801990477375, 629921975126394617164575, 12801990477375, 2731135, 255, 1
%p A176791 := proc(n,m)
%p if n >= 2*m then
%p binomial(2^n-1,2^m-1) ;
%p else
%p procname(n,n-m) ;
%p end if:
%p end proc: # _R. J. Mathar_, Jan 29 2012
%t t[n_, m_] := If[Floor[n/2] >= m, Binomial[2^n - 1, 2^m - 1], Binomial[2^n - 1, 2^(n - m) - 1]];
%t Table[Table[t[n, m], {m, 0, n}], {n, 0, 10}];
%t Flatten[%]
%Y Cf. A174387.
%K nonn,tabl,easy
%O 0,5
%A _Roger L. Bagula_, Apr 26 2010
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