%I A156224
%S A156224 1,1,1,1,4,1,3,10,10,3,3,18,22,18,3,5,28,58,58,28,5,7,46,103,158,103,46,
%T A156224 7,9,68,187,313,313,187,68,9,11,94,306,614,698,614,306,94,11,15,133,502,
%U A156224 1174,1636,1636,1174,502,133,15,19,188,763,2038,3358,4030,3358,2038,763
%N A156224 Triangle read by rows:t(n,m)=(Binomial[n, m]*PartitionsQ[n] + Binomial[n, 
               n - m]*(PartitionsQ[ n - m] + PartitionsQ[m])) - 2.
%C A156224 Row sums are:
%C A156224 {1, 2, 6, 26, 64, 182, 470, 1154, 2748, 6920, 16762,...}
%F A156224 t(n,m)=(Binomial[n, m]*PartitionsQ[n] + Binomial[n, n - m]*(PartitionsQ[ 
               n - m] + PartitionsQ[m])) - 2.
%e A156224 {1},
%e A156224 {1, 1},
%e A156224 {1, 4, 1},
%e A156224 {3, 10, 10, 3},
%e A156224 {3, 18, 22, 18, 3},
%e A156224 {5, 28, 58, 58, 28, 5},
%e A156224 {7, 46, 103, 158, 103, 46, 7},
%e A156224 {9, 68, 187, 313, 313, 187, 68, 9},
%e A156224 {11, 94, 306, 614, 698, 614, 306, 94, 11},
%e A156224 {15, 133, 502, 1174, 1636, 1636, 1174, 502, 133, 15},
%e A156224 {19, 188, 763, 2038, 3358, 4030, 3358, 2038, 763, 188, 19}
%t A156224 Clear[t, n, m];
%t A156224 t[n_, m_] = (Binomial[n, m]*PartitionsQ[n] + Binomial[n, n - m]*( PartitionsQ[n 
               - m] + PartitionsQ[m])) - 2;
%t A156224 Table[Table[t[n, m], {m, 0, n}], {n, 0, 10}];
%t A156224 Flatten[%]
%Y A156224 Sequence in context: A132703 A154182 A093735 this_sequence A162516 A085471 
               A064221
%Y A156224 Adjacent sequences: A156221 A156222 A156223 this_sequence A156225 A156226 
               A156227
%K A156224 nonn,tabl,uned
%O A156224 0,5
%A A156224 Roger L. Bagula (rlbagulatftn(AT)yahoo.com), Feb 06 2009