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Search: id:A069911
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| 1, 1, 1, 1, 2, 2, 3, 4, 5, 6, 8, 9, 12, 14, 17, 20, 25, 29, 35, 41, 49, 57, 68, 78, 93, 107, 125, 144, 168, 192, 223, 255, 294, 335, 385, 437, 501, 568, 647, 732, 833, 939, 1065, 1199, 1355, 1523, 1717, 1925, 2166, 2425, 2720, 3040, 3405, 3797, 4244, 4727, 5272
(list; graph; listen)
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OFFSET
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0,5
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COMMENT
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Arises from an identity of Slater's.
Number of partitions of 2*n+1 into distinct odd parts. - Vladeta Jovovic (vladeta(AT)Eunet.yu), May 08 2003
Euler transform of period 16 sequence [1,0,0,1,0,1,1,0,1,1,0,1,0,0,1,0,...]. - Michael Somos Apr 11 2004
Also number of partitions of 2n+1 such that if k is the largest part, then k occurs an odd number of times and each integer from 1 to k-1 occurs a positive even number of times. Example: a(4)=2 because we have [3,2,2,1,1] and [1,1,1,1,1,1,1,1,1]. - Emeric Deutsch (deutsch(AT)duke.poly.edu), Apr 16 2006
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REFERENCES
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G. E. Andrews et al., q-Engel series expansions and Slater's identities, Quaestiones Math., 24 (2001), 403-416.
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FORMULA
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G.f.=[H(sqrt(x))-H(-sqrt(x))]/(2sqrt(x)), where H(x)=product(1+x^(2*i-1), i=1..infinity). - Emeric Deutsch (deutsch(AT)duke.poly.edu), Apr 16 2006
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MAPLE
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h:=product(1+x^(2*i-1), i=1..60): hser:=series(h, x=0, 120): seq(coeff(hser, x^(2*n+1)), n=0..56); - Emeric Deutsch (deutsch(AT)duke.poly.edu), Apr 16 2006
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PROGRAM
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(PARI) {a(n)=local(A); if(n<0, 0, n=2*n+1; A=x*O(x^n); -polcoeff( eta(x+A)/eta(x^2+A), n))} /* Michael Somos Jul 18 2006 */
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CROSSREFS
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Cf. A069908, A069909, A069910.
Cf. A000700(2n+1)=a(n). A081362(2n+1)=-a(n).
Sequence in context: A029013 A114096 A008582 this_sequence A027196 A100928 A034140
Adjacent sequences: A069908 A069909 A069910 this_sequence A069912 A069913 A069914
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KEYWORD
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nonn
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AUTHOR
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njas, May 05 2002
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