A176565 - OEIS

%I #2 Mar 30 2012 17:34:40

%S 1,1,1,1,0,1,1,-6,-6,1,1,-64,-84,-64,1,1,-454,-636,-636,-454,1,1,

%T -7996,-10933,-11648,-10933,-7996,1,1,-116264,-154904,-165852,-165852,

%U -154904,-116264,1,1,-4292122,-5475909,-5769895,-5823025,-5769895,-5475909

%N A symmetrical triangle:t(n,m)=Binomial[PartitionsP[n] + m, m] + Binomial[PartitionsP[n] + n - m, n - m] - (Binomial[PartitionsP[n] + 0, 0] + Binomial[PartitionsP[ n] + n - 0, n - 0]) + 1

%C Row sums are:

%C {1, 2, 2, -10, -210, -2178, -49504, -874038, -36898875, -1572273560,

%C -135022067180,...}.

%F t(n,m)=Binomial[PartitionsP[n] + m, m] + Binomial[PartitionsP[n] + n - m, n - m] - (Binomial[PartitionsP[n] + 0, 0] + Binomial[PartitionsP[ n] + n - 0, n - 0]) + 1

%e {1},

%e {1, 1},

%e {1, 0, 1},

%e {1, -6, -6, 1},

%e {1, -64, -84, -64, 1},

%e { 1, -454, -636, -636, -454, 1},

%e {1, -7996, -10933, -11648, -10933, -7996, 1},

%e {1, -116264, -154904, -165852, -165852, -154904, -116264, 1},

%e {1, -4292122, -5475909, -5769895, -5823025, -5769895, -5475909, -4292122, 1},

%e {1, -163011609, -201619164, -209961884, -211544124, -211544124, -209961884, -201619164, -163011609, 1},

%e {1, -12777711827, -15283144624, -15734109446, -15807589523, -15816956342, -15807589523, -15734109446, -15283144624, -12777711827, 1}

%t t[n_, m_] = Binomial[PartitionsP[n] + m, m] + Binomial[PartitionsP[n] + n - m, n - m] - (Binomial[PartitionsP[n] + 0, 0] + Binomial[PartitionsP[ n] + n - 0, n - 0]) + 1;

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

%t Flatten[%]

%K sign,tabl,uned

%O 0,8

%A _Roger L. Bagula_, Apr 20 2010