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Search: id:A141724
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| A141724 |
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A triangle of coefficients of a double sum skew 4th level multinomial : t(n,m,k,l)=Sum[Sum[Multinomial[n - m - k - l, m, k, l], {l, 0, k}], {k, 0, m}]. |
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+0
1
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| 1, 1, 1, 1, 4, 1, 1, 15, 6, 1, 1, 40, 36, 8, 1, 1, 85, 160, 60, 10, 1, 1, 156, 615, 340, 90, 12, 1, 1, 259, 2016, 1715, 595, 126, 14, 1, 1, 400, 5656, 7616, 3500, 952, 168, 16, 1, 1, 585, 13896, 30408, 18396, 6300, 1428, 216, 18, 1, 1, 820, 30645, 109320, 88620, 37044
(list; graph; listen)
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OFFSET
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1,5
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COMMENT
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Row sums are:
{1, 2, 6, 23, 86, 317, 1215, 4727, 18310, 71249, 279281}.
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FORMULA
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t(n,m,k,l)=Sum[Sum[Multinomial[n - m - k - l, m, k, l], {l, 0, k}], {k, 0, m}].
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EXAMPLE
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{1},
{1, 1},
{1, 4, 1},
{1, 15, 6, 1},
{1, 40, 36, 8, 1},
{1, 85, 160, 60, 10, 1},
{1, 156, 615, 340, 90, 12, 1},
{1, 259, 2016, 1715, 595, 126, 14, 1},
{1, 400, 5656, 7616, 3500, 952, 168, 16, 1},
{1, 585, 13896, 30408, 18396, 6300, 1428, 216, 18, 1},
{1, 820, 30645, 109320, 88620, 37044, 10500, 2040, 270, 20, 1},
{1, 1111, 61930, 352605, 393030, 200508, 67914, 16500, 2805, 330, 22, 1}
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MATHEMATICA
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t[n_, m_, k_, l_] = Multinomial[n - m - k - l, m, k, l]; Table[Table[Sum[Sum[t[n, m, k, l], {l, 0, k}], {k, 0, m}], {m, 0, n}], {n, 0, 11}]; Flatten[%]
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CROSSREFS
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Cf A065109.
Sequence in context: A050154 A058711 A157013 this_sequence A157211 A116469 A156599
Adjacent sequences: A141721 A141722 A141723 this_sequence A141725 A141726 A141727
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KEYWORD
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nonn,uned
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AUTHOR
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Roger L. Bagula (rlbagulatftn(AT)yahoo.com), Sep 12 2008
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