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Search: id:A026833
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| A026833 |
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Number of partitions of n into distinct parts, the least being even. |
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+0
1
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| 0, 1, 0, 1, 1, 2, 1, 2, 3, 4, 4, 5, 6, 8, 9, 11, 14, 16, 18, 22, 26, 31, 36, 42, 49, 57, 66, 76, 88, 102, 116, 134, 154, 176, 201, 229, 260, 296, 336, 381, 432, 488, 550, 622, 700, 788, 886, 994, 1115, 1250, 1399, 1564, 1748, 1952, 2176
(list; graph; listen)
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OFFSET
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1,6
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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 occurs an even number of times and each of the numbers 1,2,...,k-1 occurs at least once. Example: a(10)=4 because we have [3,3,2,1,1],[2,2,2,2,1,1],[2,2,1,1,1,1,1,1], and [1,1,1,1,1,1,1,1,1,1]. - Emeric Deutsch (deutsch(AT)duke.poly.edu), Mar 30 2006
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FORMULA
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G.f.: Sum_{k>=2} ((-1)^k*(-1+Product_{i>=k} (1+x^i))). - Vladeta Jovovic (vladeta(AT)Eunet.yu), Aug 26 2003
G.f.=sum(x^(2k)*product(1+x^j, j=2k+1..infinity), k=1..infinity). G.f.=sum(x^(k(k+3)/2)/[(1+x^k)*product(1-x^j, j=1..k)], k=1..infinity). - Emeric Deutsch (deutsch(AT)duke.poly.edu), Mar 30 2006
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EXAMPLE
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a(10)=4 because we have [10],[8,2],[6,4], and [5,3,2].
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MAPLE
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g:=sum(x^(2*k)*product(1+x^j, j=2*k+1..60), k=1..60): gser:=series(g, x=0, 58): seq(coeff(gser, x^n), n=1..55); - Emeric Deutsch (deutsch(AT)duke.poly.edu), Mar 30 2006
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CROSSREFS
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Cf. A026832.
Sequence in context: A030383 A031231 A030562 this_sequence A056882 A035534 A082854
Adjacent sequences: A026830 A026831 A026832 this_sequence A026834 A026835 A026836
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KEYWORD
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nonn
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AUTHOR
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Clark Kimberling (ck6(AT)evansville.edu)
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