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Search: id:A115029
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| A115029 |
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Number of partitions of n such that all parts, with the possible exception of the smallest, appear only once. |
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+0
1
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| 1, 2, 3, 5, 6, 10, 12, 17, 22, 29, 36, 48, 59, 73, 93, 114, 139, 171, 207, 250, 304, 361, 432, 517, 613, 722, 856, 1005, 1178, 1382, 1612, 1875, 2184, 2528, 2927, 3386, 3900, 4486, 5159, 5916, 6772, 7749, 8843, 10078
(list; graph; listen)
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OFFSET
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1,2
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COMMENT
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Also number of partitions of n such that if k is the largest part, then k and all integers from 1 to some integer m, 0<=m<k, occur any number of times (if m = 0, then partition consists only of k's). Example: a(5)=6 because we have [5],[4,1],[3,1,1],[2,2,1],[2,1,1,1], and [1,1,1,1,1] ([3,2] does not qualify). - Emeric Deutsch (deutsch(AT)duke.poly.edu), Apr 19 2006
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FORMULA
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Sum(x^k/(1-x^k)*Product(1+x^i,i=k+1..infinity),k=1..infinity).
G.f.=sum((x^k/(1-x^k))*sum(x^(m(m+1)/2)/product(1-x^i, i=1..m), m=0..k-1), k=1..infinity). - Emeric Deutsch (deutsch(AT)duke.poly.edu), Apr 19 2006
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EXAMPLE
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a(5)=6 because we have [5],[4,1],[3,2],[3,1,1],[2,1,1,1], and [1,1,1,1,1] ([2,2,1] does not qualify).
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MAPLE
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g:=sum(x^k/(1-x^k)*product(1+x^i, i=k+1..90), k=1..90): gser:=series(g, x=0, 50): seq(coeff(gser, x^n), n=1..44); - Emeric Deutsch (deutsch(AT)duke.poly.edu), Apr 19 2006
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CROSSREFS
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Cf. A034296.
Sequence in context: A027593 A007211 A130900 this_sequence A023025 A130898 A088314
Adjacent sequences: A115026 A115027 A115028 this_sequence A115030 A115031 A115032
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KEYWORD
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easy,nonn
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AUTHOR
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Vladeta Jovovic (vladeta(AT)Eunet.yu), Feb 25 2006; corrected Mar 05 2006
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