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A131942
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Number of partitions of n in which each odd part has odd multiplicity.
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8
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1, 1, 1, 3, 3, 6, 6, 11, 13, 21, 24, 35, 44, 59, 74, 99, 126, 158, 202, 250, 320, 392, 495, 598, 758, 908, 1134, 1358, 1685, 2003, 2466, 2925, 3576, 4234, 5129, 6064, 7308, 8612, 10305, 12135, 14443, 16963, 20085, 23548, 27754, 32482, 38105, 44503, 52042
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OFFSET
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0,4
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REFERENCES
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Drake, Brian, Limits of areas under lattice paths. Discrete Math. 309 (2009), no. 12, 3936-3953.
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LINKS
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Brian Drake, Table of n, a(n) for n = 0..100
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FORMULA
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G.f.: product_{n=1..inf} (1+q^(2n-1)-q^(4n-2))/((1-q^(2n))(1-q^(4n-2)))
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EXAMPLE
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a(5)=6 because 5, 4+1, 3+2, 2+2+1, 2+1+1+1 and 1+1+1+1+1 have all odd parts with odd multiplicity. The partition 3+1+1 is the partition of 5 which is not counted.
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MAPLE
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A:= series(product( 1/(1-q^(2*n)) *(1+q^(2*n-1)-q^(4*n-2))/(1-q^(4*n-2)), n=1..15), q, 25): seq(coeff(A, q, i), i=0..24);
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CROSSREFS
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Cf. A000041, A015128, A006950, A046682.
Sequence in context: A088528 A220153 A219627 * A200905 A117775 A021301
Adjacent sequences: A131939 A131940 A131941 * A131943 A131944 A131945
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KEYWORD
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easy,nonn
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AUTHOR
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Brian Drake (bdrake(AT)brandeis.edu), Jul 30 2007
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STATUS
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approved
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