Search: id:A069911
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%I A069911
%S A069911 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,
%T A069911 144,168,192,223,255,294,335,385,437,501,568,647,732,833,939,1065,1199,
%U A069911 1355,1523,1717,1925,2166,2425,2720,3040,3405,3797,4244,4727,5272
%N A069911 Expansion of Product_{i in A069909} 1/(1-x^i).
%C A069911 Arises from an identity of Slater's.
%C A069911 Number of partitions of 2*n+1 into distinct odd parts. - Vladeta Jovovic 
               (vladeta(AT)eunet.rs), May 08 2003
%C A069911 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
%C A069911 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
%D A069911 G. E. Andrews et al., q-Engel series expansions and Slater's identities, 
               Quaestiones Math., 24 (2001), 403-416.
%F A069911 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
%p A069911 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
%o A069911 (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 */
%Y A069911 Cf. A069908, A069909, A069910.
%Y A069911 Cf. A000700(2n+1)=a(n). A081362(2n+1)=-a(n).
%Y A069911 Sequence in context: A029013 A114096 A008582 this_sequence A027196 A100928 
               A034140
%Y A069911 Adjacent sequences: A069908 A069909 A069910 this_sequence A069912 A069913 
               A069914
%K A069911 nonn
%O A069911 0,5
%A A069911 N. J. A. Sloane (njas(AT)research.att.com), May 05 2002

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