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A026805
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Number of partitions of n in which the least part is even.
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5
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0, 1, 0, 2, 1, 3, 2, 6, 5, 9, 9, 16, 17, 26, 28, 42, 48, 66, 77, 105, 122, 160, 189, 245, 290, 368, 436, 547, 650, 804, 954, 1174, 1390, 1693, 2004, 2425, 2865, 3445, 4060, 4858, 5716, 6802, 7986, 9468, 11087, 13088, 15298, 17995, 20987
(list; graph; refs; listen; history; internal format)
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OFFSET
| 1,4
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COMMENTS
| Also number of partitions of n in which the largest part occurs an even number of times. Example: a(6)=3 because we have [3,3],[2,2,1,1] and [1,1,1,1,1,1]. - Emeric Deutsch (deutsch(AT)duke.poly.edu), Apr 04 2006
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FORMULA
| G.f.: Sum_{k>=2} ((-1)^k*(-1+1/Product_{i>=k} (1-x^i))). a(n) = Sum_{k=2..n} (-1)^k*A026807(n, k) = A000041(n)-A026804(n). - Vladeta Jovovic (vladeta(AT)eunet.rs), Aug 26 2003
G.f.=sum(x^(2k)/product(1-x^j, j=2k..infinity), k=1..infinity). G.f.=sum(x^(2k)/[(1-x^(2k))*product(1-x^j,j=1..k-1)], k=1..infinity). - Emeric Deutsch (deutsch(AT)duke.poly.edu), Apr 04 2006
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EXAMPLE
| a(6)=3 because we have [6],[4,2] and [2,2,2].
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MAPLE
| g:=sum(x^(2*k)/(1-x^(2*k))/product(1-x^j, j=1..k-1), k=1..40): gser:=series(g, x=0, 52): seq(coeff(gser, x, n), n=1..49); - Emeric Deutsch (deutsch(AT)duke.poly.edu), Apr 04 2006
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CROSSREFS
| Sequence in context: A165045 A164768 A006208 * A022477 A144238 A082833
Adjacent sequences: A026802 A026803 A026804 * A026806 A026807 A026808
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KEYWORD
| nonn
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AUTHOR
| Clark Kimberling (ck6(AT)evansville.edu)
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