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Search: id:A060016
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| A060016 |
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Triangle T(n,k) = number of partitions of n into k distinct parts, 1<=k<=n. |
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+0
9
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| 1, 1, 0, 1, 1, 0, 1, 1, 0, 0, 1, 2, 0, 0, 0, 1, 2, 1, 0, 0, 0, 1, 3, 1, 0, 0, 0, 0, 1, 3, 2, 0, 0, 0, 0, 0, 1, 4, 3, 0, 0, 0, 0, 0, 0, 1, 4, 4, 1, 0, 0, 0, 0, 0, 0, 1, 5, 5, 1, 0, 0, 0, 0, 0, 0, 0, 1, 5, 7, 2, 0, 0, 0, 0, 0, 0, 0, 0, 1, 6, 8, 3, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 6, 10, 5, 0, 0, 0, 0, 0, 0, 0, 0, 0
(list; table; graph; listen)
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OFFSET
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1,12
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COMMENT
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Also number of partitions of n-k(k+1)/2 into at most k parts (not necessarily distinct).
A025147(n) = Sum(a(n-k+1,k-1): 1<k<=floor((n+2)/2). - Reinhard Zumkeller (reinhard.zumkeller(AT)gmail.com), Nov 04 2007
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REFERENCES
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M. Abramowitz and I. A. Stegun, eds., Handbook of Mathematical Functions, National Bureau of Standards Applied Math. Series 55, 1964 (and various reprintings), p. 831.
L. Comtet, Advanced Combinatorics, Reidel, 1974, pp. 94, 96 and 307.
F. N. David, M. G. Kendall and D. E. Barton, Symmetric Function and Allied Tables, Cambridge, 1966, p. 219.
D. S. Mitrinovic et al., Handbook of Number Theory, Kluwer, Section XIV.2, p. 493.
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LINKS
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M. Abramowitz and I. A. Stegun, eds., Handbook of Mathematical Functions, National Bureau of Standards, Applied Math. Series 55, Tenth Printing, December 1972 [alternative scanned copy].
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FORMULA
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T(n, k) =T(n-k, k)+T(n-k, k-1) [with T(n, 0)=1 if n=0 and 0 otherwise].
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EXAMPLE
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1; 1,0; 1,1,0; 1,1,0,0; 1,2,0,0,0; ...
T(8,3)=2 since 8 can be written in 2 ways as the sum of 3 distinct positive integers: 5+2+1 and 4+3+1.
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CROSSREFS
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Columns (offset) include A057427, A004526, A001399, A001400, A001401, etc. Cf. A000009 (row sums), A008289 (without zeros), A030699 (row maximum), A008284 (partition triangle including duplications).
See A008289 for another version.
Sequence in context: A025891 A120630 A089605 this_sequence A117408 A079100 A123262
Adjacent sequences: A060013 A060014 A060015 this_sequence A060017 A060018 A060019
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KEYWORD
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nonn,tabl,nice,easy
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AUTHOR
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njas
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EXTENSIONS
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More terms, recurrence, etc. from Henry Bottomley (se16(AT)btinternet.com), Mar 26 2001
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