%I A142473
%S A142473 1,1,2,4,6,6,36,44,36,24,576,600,420,240,120,14400,13152,8100,4080,1800,
               720,
%T A142473 518400,423360,233856,105840,42000,15120,5040,25401600,18817920,9455040,
               3898944,
%U A142473 1411200,463680,141120,40320,1625702400,1104606720,510295680,193777920,
               64653120
%V A142473 1,-1,2,4,-6,6,-36,44,-36,24,576,-600,420,-240,120,-14400,13152,-8100,
               4080,-1800,720,
%W A142473 518400,-423360,233856,-105840,42000,-15120,5040,-25401600,18817920,-9455040,
               3898944,
%X A142473 -1411200,463680,-141120,40320,1625702400,-1104606720,510295680,-193777920,
               64653120
%N A142473 A division triangle sequence of the Stirling numbers of the first kind 
               by the binomial ( Pascal's triangle): t(n,m)=n!*StirlingS1[n, m]/
               Binomial[n, m].
%C A142473 Row sums are:
%C A142473 {1, 1, 4, -4, 276, -6348, 254976, -13188096, 887086080, -74869297920}.
%D A142473 t(n,m)=n!*StirlingS1[n, m]/Binomial[n, m].
%F A142473 t(n,m)=n!*StirlingS1[n, m]/Binomial[n, m].
%e A142473 {1},
%e A142473 {-1, 2},
%e A142473 {4, -6, 6},
%e A142473 {-36, 44, -36, 24},
%e A142473 {576, -600, 420, -240, 120},
%e A142473 {-14400, 13152, -8100, 4080, -1800, 720},
%e A142473 {518400, -423360, 233856, -105840, 42000, -15120, 5040},
%e A142473 {-25401600, 18817920, -9455040, 3898944, -1411200, 463680, -141120, 40320},
%e A142473 {1625702400, -1104606720, 510295680, -193777920, 64653120, -19595520, 
               5503680, -1451520, 362880},
%e A142473 {-131681894400, 82783088640, -35462448000, 12505190400, -3878280000, 
               1093357440, -285768000, 70156800, -16329600, 3628800}
%t A142473 t[n_, m_] = n!*StirlingS1[n, m]/Binomial[n, m]; Table[Table[t[n, m], 
               {m, 1, n}], {n, 1, 10}]; Flatten[%]
%Y A142473 Sequence in context: A087459 A123258 A104968 this_sequence A132426 A072646 
               A162672
%Y A142473 Adjacent sequences: A142470 A142471 A142472 this_sequence A142474 A142475 
               A142476
%K A142473 sign,uned
%O A142473 1,3
%A A142473 Roger L. Bagula and Gary W. Adamson (rlbagulatftn(AT)yahoo.com), Sep 
               21 2008