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Search: id:A156052
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| A156052 |
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Triangle read by rows: t(n,m)=Binomial[n, m]/Beta[n + 1, n - m + 1] + Binomial[n, n - m]/Beta[n + 1, m + 1]. |
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+0
1
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| 2, 8, 8, 33, 48, 33, 144, 240, 240, 144, 635, 1240, 1260, 1240, 635, 2778, 6510, 6720, 6720, 6510, 2778, 12019, 33600, 38430, 33600, 38430, 33600, 12019, 51488, 168672, 223776, 184800, 184800, 223776, 168672, 51488, 218799, 824400, 1275120, 1119888
(list; table; graph; listen)
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OFFSET
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0,1
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COMMENT
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Row sums are:
{2, 16, 114, 768, 5010, 32016, 201698, 1257472, 7777314, 47800080, 292292946,...}.
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FORMULA
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t(n,m)=Binomial[n, m]/Beta[n + 1, n - m + 1] + Binomial[n, n - m]/Beta[n + 1, m + 1].
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EXAMPLE
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{2},
{8, 8},
{33, 48, 33},
{144, 240, 240, 144},
{635, 1240, 1260, 1240, 635},
{2778, 6510, 6720, 6720, 6510, 2778},
{12019, 33600, 38430, 33600, 38430, 33600, 12019},
{51488, 168672, 223776, 184800, 184800, 223776, 168672, 51488},
{218799, 824400, 1275120, 1119888, 900900, 1119888, 1275120, 824400, 218799},
{923790, 3939210, 7025040, 6966960, 5045040, 5045040, 6966960, 7025040, 3939210, 923790},
{3879887, 18476920, 37451700, 42488160, 31741710, 24216192, 31741710, 42488160, 37451700, 18476920, 3879887}
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MATHEMATICA
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Clear[f];
f[n_, m_] = Binomial[ n, m]/Beta[n + 1, n - m + 1] + Binomial[n, n - m]/Beta[n + 1, m + 1];
Table[Table[f[n, m], {m, 0, n}], {n, 0, 10}];
Flatten[%]
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CROSSREFS
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Sequence in context: A116471 A146749 A064231 this_sequence A083523 A009181 A009666
Adjacent sequences: A156049 A156050 A156051 this_sequence A156053 A156054 A156055
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KEYWORD
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nonn,tabl,uned
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AUTHOR
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Roger L. Bagula (rlbagulatftn(AT)yahoo.com), Feb 02 2009
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