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Search: id:A036038
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| A036038 |
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Triangle of multinomial coefficients. |
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+0
28
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| 1, 1, 2, 1, 3, 6, 1, 4, 6, 12, 24, 1, 5, 10, 20, 30, 60, 120, 1, 6, 15, 20, 30, 60, 90, 120, 180, 360, 720, 1, 7, 21, 35, 42, 105, 140, 210, 210, 420, 630, 840, 1260, 2520, 5040, 1, 8, 28, 56, 70, 56, 168, 280, 420, 560, 336, 840, 1120, 1680, 2520, 1680, 3360, 5040, 6720
(list; graph; listen)
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OFFSET
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1,3
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COMMENT
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The number of terms in the n-th row is the number of partition of n. - Amarnath Murthy (amarnath_murthy(AT)yahoo.com), Sep 21 2002
For each n, the partitions are ordered by length and then lexicographically, which is different from the usual practice of ordering all partitions lexicographically. (T. D. Noe)
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REFERENCES
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Abramowitz and Stegun, Handbook, p. 831, column labeled "M_1".
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LINKS
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T. D. Noe, Rows n=1..25 of triangle, flattened
M. Abramowitz and I. A. Stegun, eds., Handbook of Mathematical Functions, National Bureau of Standards, Applied Math. Series 55, Tenth Printing, 1972 [alternative scanned copy].
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EXAMPLE
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1; 1,2; 1,3,6; 1,4,6,12,24; 1,5,10,20,30,60,120; ...
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MATHEMATICA
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Flatten[Table[Apply[Multinomial, Reverse[Sort[Partitions[i], Length[ #1]>Length[ #2]&]], {1}], {i, 9}]] - T. D. Noe (noe(AT)sspectra.com), Nov 03 2006
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CROSSREFS
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Cf. A036036-A036040. Different from A078760. Row sums give A005651.
Sequence in context: A081520 A010251 A051537 this_sequence A078760 A103280 A046899
Adjacent sequences: A036035 A036036 A036037 this_sequence A036039 A036040 A036041
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KEYWORD
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nonn,easy,nice,tabf
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AUTHOR
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N. J. A. Sloane (njas(AT)research.att.com).
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EXTENSIONS
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More terms from David W. Wilson (davidwwilson(AT)comcast.net) and wouter.meeussen(AT)pandora.be.
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