Search: id:A156991
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%I A156991
%S A156991 1,0,1,0,2,6,0,6,24,60,0,24,120,360,840,0,120,720,2520,6720,15120,0,720,
%T A156991 5040,20160,60480,151200,332640,0,5040,40320,181440,604800,1663200,
%U A156991 3991680,8648640,0,40320,362880,1814400,6652800,19958400,51891840
%N A156991 A triangular sequence:t(n,m)=n!*Binomial[n + m - 1, n]
%C A156991 Row sums are:
%C A156991 {1, 1, 8, 90, 1344, 25200, 570240, 15135120, 461260800, 15878903040,
%C A156991 609493248000,...}.
%C A156991 This sequence is the ordered occupancy form from Riordan.
%C A156991 Apart from the left column of (essentially) zeros, the same as A105725. 
               [From R. J. Mathar (mathar(AT)strw.leidenuniv.nl), Mar 02 2009]
%D A156991 J. Riordan, An Introduction to Combinatorial Analysis, Wiley, 1958, p. 
               98
%F A156991 t(n,m)=n!*Binomial[n + m - 1, n].
%e A156991 {1},
%e A156991 {0, 1},
%e A156991 {0, 2, 6},
%e A156991 {0, 6, 24, 60},
%e A156991 {0, 24, 120, 360, 840},
%e A156991 {0, 120, 720, 2520, 6720, 15120},
%e A156991 {0, 720, 5040, 20160, 60480, 151200, 332640},
%e A156991 {0, 5040, 40320, 181440, 604800, 1663200, 3991680, 8648640},
%e A156991 {0, 40320, 362880, 1814400, 6652800, 19958400, 51891840, 121080960, 259459200},
%e A156991 {0, 362880, 3628800, 19958400, 79833600, 259459200, 726485760, 1816214400, 
               4151347200, 8821612800}, {0, 3628800, 39916800, 239500800, 1037836800, 
               3632428800, 10897286400, 29059430400, 70572902400, 158789030400, 
               335221286400}
%t A156991 Clear[t, n, m];
%t A156991 t[n_, m_] = n!*Binomial[n + m - 1, n];
%t A156991 Table[Table[t[n, m], {m, 0, n}], {n, 0, 10}];
%t A156991 Flatten[%]
%Y A156991 Sequence in context: A115252 A108431 A019967 this_sequence A065344 A131105 
               A057635
%Y A156991 Adjacent sequences: A156988 A156989 A156990 this_sequence A156992 A156993 
               A156994
%K A156991 nonn,tabf,uned
%O A156991 0,5
%A A156991 Roger L. Bagula (rlbagulatftn(AT)yahoo.com), Feb 20 2009

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