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Search: id:A038348
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| A038348 |
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Expansion of (1/(1-x^2))*Product((1/(1-x^(2m+1)), m=0..inf. |
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7
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| 1, 1, 2, 3, 4, 6, 8, 11, 14, 19, 24, 31, 39, 49, 61, 76, 93, 114, 139, 168, 203, 244, 292, 348, 414, 490, 579, 682, 801, 938, 1097, 1278, 1487, 1726, 1999, 2311, 2667, 3071, 3531, 4053, 4644, 5313, 6070, 6923, 7886, 8971, 10190, 11561
(list; graph; listen)
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OFFSET
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0,3
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COMMENT
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Number of partitions of n+2 with exactly one even part. - Vladeta Jovovic (vladeta(AT)Eunet.yu), Sep 10 2003
Number of partitions of n with at most one even part. - Vladeta Jovovic (vladeta(AT)Eunet.yu), Sep 10 2003
Also total number of parts, counted without multiplicity, in all partitions of n into odd parts, offset 1. - Vladeta Jovovic (vladeta(AT)Eunet.yu), Mar 27 2005
a(n)=Sum(k*A116674(n+1,k),k>=1). - Emeric Deutsch (deutsch(AT)duke.poly.edu), Feb 22 2006
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LINKS
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P. Flajolet and B. Salvy, Euler sums and contour integral representations, Experimental Mathematics, Vol. 7 Issue 1 (1998)
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FORMULA
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a(n) = A036469(n)-a(n-1) = Sum_{k=0..n}(-1)^k*A036469(n-k). - Vladeta Jovovic (vladeta(AT)Eunet.yu), Sep 10 2003
a(n) = A000009(n)+a(n-2). - Vladeta Jovovic (vladeta(AT)Eunet.yu), Feb 10 2004
G.f.=1/[(1-x^2)product(1-x^(2j-1),j=1..infinity)]. - Emeric Deutsch (deutsch(AT)duke.poly.edu), Feb 22 2006
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MAPLE
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f:=1/(1-x^2)/product(1-x^(2*j-1), j=1..32): fser:=series(f, x=0, 62): seq(coeff(fser, x, n), n=0..58); - Emeric Deutsch (deutsch(AT)duke.poly.edu), Feb 22 2006
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CROSSREFS
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Cf. A067588.
Cf. A116674.
Sequence in context: A062464 A053270 A003412 this_sequence A035945 A094707 A117995
Adjacent sequences: A038345 A038346 A038347 this_sequence A038349 A038350 A038351
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KEYWORD
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nonn
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AUTHOR
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njas
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