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Triangle t(n,m)= (m+1)^n*binomial(n,m) if m <= n/2, otherwise t(n,m) = t(n,n-m).
1

%I #9 Oct 13 2012 20:51:57

%S 1,1,1,1,8,1,1,24,24,1,1,64,486,64,1,1,160,2430,2430,160,1,1,384,

%T 10935,81920,10935,384,1,1,896,45927,573440,573440,45927,896,1,1,2048,

%U 183708,3670016,27343750,3670016,183708,2048,1,1,4608,708588,22020096

%N Triangle t(n,m)= (m+1)^n*binomial(n,m) if m <= n/2, otherwise t(n,m) = t(n,n-m).

%C Row sums are 1, 2, 10, 50, 616, 5182, 104560, 1240528, 35055296, 537654086, 19596031984,...

%C This is obtained by taking the absolute value of the first half of each row of A075513 and defining the second half by mirror symmetry.

%e 1;

%e 1, 1;

%e 1, 8, 1;

%e 1, 24, 24, 1;

%e 1, 64, 486, 64, 1;

%e 1, 160, 2430, 2430, 160, 1;

%e 1, 384, 10935, 81920, 10935, 384, 1;

%e 1, 896, 45927, 573440, 573440, 45927, 896, 1;

%e 1, 2048, 183708, 3670016, 27343750, 3670016, 183708, 2048, 1;

%p A167034 := proc(n,m)

%p if m <= n/2 then

%p (m+1)^n*binomial(n,m) ;

%p else

%p procname(n,n-m) ;

%p end if;

%p end proc: # _R. J. Mathar_, Oct 13 2012

%t T[m_, n_] = If[Floor[m/2] >= n, (n + 1)^m*Binomial[m, n], (m - n + 1)^m*Binomial[m, m - n]]

%t Flatten[Table[Table[T[m, n], {n, 0, m}], {m, 0, 10}]]

%K nonn,easy,tabl

%O 0,5

%A _Roger L. Bagula_ and _Mats Granvik_, Oct 27 2009