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%I #2 Mar 30 2012 17:34:39
%S 1,1,1,1,4,1,1,11,11,1,1,36,70,36,1,1,133,394,394,133,1,1,518,2063,
%T 3092,2063,518,1,1,2055,10261,20515,20515,10261,2055,1,1,8200,49180,
%U 122936,163910,122936,49180,8200,1,1,32777,229412,688212,1147006,1147006
%N Triangle T(n,m) read by rows: T(n,0)=T(n,n)=1, else T(n,m)= binomial(n,m) + 2^(2*n-3) *binomial(n-2,m-1).
%C Row sums are 1, 2, 6, 24, 144, 1056, 8256, 65664, 524544, 4194816, 3355545,...
%e 1;
%e 1, 1;
%e 1, 4, 1;
%e 1, 11, 11, 1;
%e 1, 36, 70, 36, 1;
%e 1, 133, 394, 394, 133, 1;
%e 1, 518, 2063, 3092, 2063, 518, 1;
%e 1, 2055, 10261, 20515, 20515, 10261, 2055, 1;
%e 1, 8200, 49180, 122936, 163910, 122936, 49180, 8200, 1;
%e 1, 32777, 229412, 688212, 1147006, 1147006, 688212, 229412, 32777, 1;
%e 1, 131082, 1048621, 3670136, 7340242, 9175292, 7340242, 3670136, 1048621, 131082, 1;
%t t[n_, m_, q_] := If[m == 0 || m == n, 1, Binomial[n, m] + q^(2*n - 3)*Binomial[n - 2, m - 1]];
%t Table[Table[Table[t[n, m, q], {m, 0, n}], {n, 0, 10}], {q, 1, 10}];
%t Table[Flatten[Table[Table[t[n, m, q], {m, 0, n}], {n, 0, 10}]], {q, 1, 10}]
%Y cf. A008292
%K nonn,tabl
%O 0,5
%A _Roger L. Bagula_, Feb 11 2010
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