%I A137312
%S A137312 1,0,2,0,2,4,0,4,12,8,0,12,44,48,16,0,48,200,280,160,32,0,240,1096,1800,
               1360,
%T A137312 480,64,0,1440,7056,12992,11760,5600,1344,128,0,10080,52272,105056,108304,
               62720,
%U A137312 20608,3584,256,0,80640,438336,944992,1076544,718368,290304,69888,9216,
               512,0
%V A137312 1,0,2,0,-2,4,0,4,-12,8,0,-12,44,-48,16,0,48,-200,280,-160,32,0,-240,1096,
               -1800,1360,
%W A137312 -480,64,0,1440,-7056,12992,-11760,5600,-1344,128,0,-10080,52272,-105056,
               108304,-62720,
%X A137312 20608,-3584,256,0,80640,-438336,944992,-1076544,718368,-290304,69888,
               -9216,512,0
%N A137312 A triangular sequence from a coefficients of generalized factorial polynomial 
               recursion from Roman:a=1/2; p(x, n) = (x/a - (n - 1))*p(x, n - 1).
%C A137312 Row sums are:
%C A137312 {1, 2, 2, 0, 0, 0, 0, 0, 0, 0, 0}
%D A137312 Steve Roman, The Umbral Calculus, Dover Publications, New York (1984), 
               pp. 56-57
%F A137312 p(x,0)=1;p(x,1)=x/a;a=1/2; p(x, n) = (x/a - (n - 1))*p(x, n - 1).
%e A137312 {1},
%e A137312 {0, 2},
%e A137312 {0, -2, 4},
%e A137312 {0, 4, -12, 8},
%e A137312 {0, -12, 44, -48, 16},
%e A137312 {0, 48, -200, 280, -160,32},
%e A137312 {0, -240, 1096, -1800, 1360, -480, 64},
%e A137312 {0, 1440, -7056, 12992, -11760, 5600, -1344, 128},
%e A137312 {0, -10080,52272, -105056, 108304, -62720, 20608, -3584, 256},
%e A137312 {0, 80640, -438336, 944992, -1076544,718368, -290304, 69888, -9216, 512},
%e A137312 {0, -725760, 4106304, -9381600,11578880, -8618400, 4049472, -1209600, 
               222720, -23040, 1024}
%t A137312 a = 1/2; p[x, 0] = 1; p[x, 1] = x/a; p[x_, n_] := p[x, n] = (x/a - (n 
               - 1))*p[x, n - 1]; Table[ExpandAll[p[x, n]], {n, 0, 10}]; a0 = Table[CoefficientList[p[x, 
               n], x], {n, 0, 10}]; Flatten[a0]
%Y A137312 Apart from signs, same as A137320.
%Y A137312 Sequence in context: A126440 A131186 A137320 this_sequence A143507 A071961 
               A120557
%Y A137312 Adjacent sequences: A137309 A137310 A137311 this_sequence A137313 A137314 
               A137315
%K A137312 uned,tabl,sign
%O A137312 1,3
%A A137312 Roger L. Bagula (rlbagulatftn(AT)yahoo.com), Apr 20 2008