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