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%I #2 Mar 30 2012 17:34:39
%S 1,1,1,1,-4,1,1,-3,-3,1,1,-48,132,-48,1,1,70,-150,-150,70,1,1,-810,
%T 5385,-9000,5385,-810,1,1,4893,-33369,31115,31115,-33369,4893,1,1,
%U -40544,374920,-845152,947660,-845152,374920,-40544,1,1,362556,-3925368
%N A symmetrical triangular sequence:t(n,m)=(StirlingS1[n, m] + StirlingS1[n, n - m])*Binomial[n, m] - (StirlingS1[n, 0] + StirlingS1[n, n - 0])* Binomial[n, 0] + 1
%C Row sums are:
%C {1, 2, -2, -4, 38, -158, 152, 5280, -73890, 658742, -3723898,...}.
%F t(n,m)=(StirlingS1[n, m] + StirlingS1[n, n - m])*Binomial[n, m] - (StirlingS1[n, 0] + StirlingS1[n, n - 0])* Binomial[n, 0] + 1
%e {1},
%e {1, 1},
%e {1, -4, 1},
%e {1, -3, -3, 1},
%e {1, -48, 132, -48, 1},
%e {1, 70, -150, -150, 70, 1},
%e {1, -810, 5385, -9000, 5385, -810, 1},
%e {1, 4893, -33369, 31115, 31115, -33369, 4893, 1},
%e {1, -40544, 374920, -845152, 947660, -845152, 374920, -40544, 1},
%e {1, 362556, -3925368, 9541392, -5649210, -5649210, 9541392, -3925368, 362556, 1},
%e {1, -3629250, 46235070, -141858000, 165260130, -135739800, 165260130, -141858000, 46235070, -3629250, 1}
%t t[n_,m_]=( StirlingS1[n,m]+StirlingS1[n,n-m])*Binomial[n,m]-(StirlingS1[n, 0]+StirlingS1[n,n-0])*Binomial[n,0]+1;
%t Table[Table[t[n,m],{m,0,n}],{n,0,10}];
%t Flatten[%]
%Y Cf. A154843
%K sign,tabl,uned
%O 0,5
%A _Roger L. Bagula_, Mar 30 2010
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