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A067659
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Number of partitions of n into distinct parts such that number of parts is an odd number.
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4
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0, 1, 1, 1, 1, 1, 2, 2, 3, 4, 5, 6, 8, 9, 11, 14, 16, 19, 23, 27, 32, 38, 44, 52, 61, 71, 82, 96, 111, 128, 148, 170, 195, 224, 256, 293, 334, 380, 432, 491, 557, 630, 713, 805, 908, 1024, 1152, 1295, 1455, 1632, 1829, 2048, 2291, 2560, 2859, 3189, 3554, 3958, 4404
(list; graph; refs; listen; history; internal format)
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OFFSET
| 0,7
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COMMENTS
| Ramanujan theta functions: f(q) := Prod_{k>=1} (1-(-q)^k) (see A121373), phi(q) := theta_3(q) := Sum_{k=-oo..oo} q^(k^2) (A000122), psi(q) := Sum_{k=0..oo} q^(k*(k+1)/2) (A10054), chi(q) := Prod_{k>=0} (1+q^(2k+1)) (A000700).
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LINKS
| M. Somos, Introduction to Ramanujan theta functions
Eric Weisstein's World of Mathematics, Ramanujan Theta Functions
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FORMULA
| For g.f. see under A067661.
(A000009(n)-A010815(n))/2. - Vladeta Jovovic (vladeta(AT)eunet.rs), Feb 24 2002
Expansion of (1-phi(-q))/(2*chi(-q)) in powers of q where phi(),chi() are Ramanujan theta functions. - Michael Somos Feb 14 2006
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PROG
| (PARI) {a(n)=local(A); if(n<0, 0, A=x*O(x^n); polcoeff( (eta(x^2+A)/eta(x+A)-eta(x+A))/2, n))} /* Michael Somos Feb 14 2006 */
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CROSSREFS
| Sequence in context: A027198 A027197 A137793 * A153156 A017852 A029013
Adjacent sequences: A067656 A067657 A067658 * A067660 A067661 A067662
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KEYWORD
| easy,nonn
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AUTHOR
| Naohiro Nomoto (n_nomoto(AT)yabumi.com), Feb 23 2002
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