%I A005896 M2338
%S A005896 0,0,0,1,1,3,4,7,9,14,19,26,34,45,59,76,96,121,153,189,234,288,353,
%T A005896 428,519,625,752,900,1073,1274,1512,1784,2101,2470,2894,3382,3946,
%U A005896 4590,5330,6179,7144,8246,9505,10931,12552,14396,16476,18831,21495
%N A005896 Weighted count of partitions with odd parts.
%D A005896 N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, 
               Academic Press, 1995 (includes this sequence).
%D A005896 Andrews, George E. Ramanujan's "lost" notebook. V. Euler's partition 
               identity. Adv. in Math. 61 (1986), no. 2, 156-164.
%F A005896 G.f.: Sum_{n=0..inf} {S(q)-1/((1-q)(1-q^3)...(1-q^(2n+1)))}, where S(q) 
               = g.f. for A000009.
%o A005896 (PARI) /* set "infinity" */ oo = 50; /* G.f. for partitions with odd 
               parts: */ Q(n,q) = prod(k=0,n,1/(1-q^(2*k+1)), 1+q*O(q^oo)); /* G.f. 
               for A000009: */ Sq = Q(oo/2,q); /* G.f. for A005896: */ Sq0 = sum(n=0,
               oo/2, Sq-Q(n,q)); for(n=0,48,print1(polcoeff(Sq0,n)","))
%Y A005896 Cf. A000009, A005895, A003406.
%Y A005896 Sequence in context: A140208 A098390 A008763 this_sequence A147953 A163468 
               A069183
%Y A005896 Adjacent sequences: A005893 A005894 A005895 this_sequence A005897 A005898 
               A005899
%K A005896 nonn,easy,nice
%O A005896 0,6
%A A005896 N. J. A. Sloane (njas(AT)research.att.com), Simon Plouffe (simon.plouffe(AT)gmail.com)
%E A005896 More terms from Michael Somos.