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A038348
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Expansion of (1/(1-x^2))*Product(1/(1-x^(2m+1)), m=0..infinity).
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8
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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; refs; listen; history; internal format)
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OFFSET
| 0,3
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COMMENTS
| Number of partitions of n+2 with exactly one even part. - Vladeta Jovovic (vladeta(AT)eunet.rs), Sep 10 2003
Also, number of partitions of n with at most one even part. - Vladeta Jovovic (vladeta(AT)eunet.rs), 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.rs), Mar 27 2005
a(n)=Sum(k*A116674(n+1,k),k>=1). - Emeric Deutsch (deutsch(AT)duke.poly.edu), Feb 22 2006
Equals row sums of triangle A173305 [From Gary W. Adamson (qntmpkt(AT)yahoo.com), Feb 15 2010]
Equals partial sums of A025147 (observed by Jonathan Vos Post, proved by several correspondents).
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LINKS
| P. Flajolet and B. Salvy, Euler sums and contour integral representations, Experimental Mathematics, Vol. 7 Issue 1 (1998)
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FORMULA
| a(n) = A036469(n)-a(n-1) = Sum_{k=0..n}(-1)^k*A036469(n-k). - Vladeta Jovovic (vladeta(AT)eunet.rs), Sep 10 2003
a(n) = A000009(n)+a(n-2). - Vladeta Jovovic (vladeta(AT)eunet.rs), Feb 10 2004
G.f.: 1/((1-x^2)*product(j>=1, 1-x^(2*j-1) ). - Emeric Deutsch (deutsch(AT)duke.poly.edu), Feb 22 2006
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MAPLE
| 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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MATHEMATICA
| mmax = 47; CoefficientList[ Series[ (1/(1-x^2))*Product[1/(1-x^(2m+1)), {m, 0, mmax}], {x, 0, mmax}], x] (* From Jean-François Alcover, Jun 21 2011 *)
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CROSSREFS
| Cf. A067588, A116674, A173305.
Sequence in context: A062464 A053270 A003412 * A035945 A094707 A117995
Adjacent sequences: A038345 A038346 A038347 * A038349 A038350 A038351
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KEYWORD
| nonn
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AUTHOR
| N. J. A. Sloane (njas(AT)research.att.com).
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