Search: id:A006950
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%I A006950 M0524
%S A006950 1,1,1,2,3,4,5,7,10,13,16,21,28,35,43,55,70,86,105,130,161,196,236,287,
%T A006950 350,420,501,602,722,858,1016,1206,1431,1687,1981,2331,2741,3206,3740,
%U A006950 4368,5096,5922,6868,7967,9233,10670,12306,14193,16357,18803,21581
%N A006950 G.f.: Product_{k>0} (1+x^(2*k-1))/(1-x^(2*k)).
%C A006950 Number of partitions of n in which each even part occurs with even multiplicity. 
               There is no restriction on the odd parts.
%C A006950 Also the number of partitions of n into parts not congruent to 2 mod 
               4 - James A. Sellers (sellersj(AT)math.psu.edu), Feb 08, 2002
%C A006950 Coincides with the sequence of numbers of nilpotent conjugacy classes 
               in the Lie algebras o(n) of skew-symmetric n X n matrices, n=0,1,
               2,3,... (the cases n=0,1 being degenerate). This sequence, A015128 
               and A000041 together cover the nilpotent conjugacy classes in the 
               classical A,B,C,D series of Lie algebras. - Alexander Elashvili, 
               Sep 08 2003
%C A006950 Poincare series (or Molien series) for symmetric invariants in F_2(b_1, 
               b_2, ... b_n) \otimes E(e_1, e_2, ... e_n) with b_i 2-dimensional, 
               e_i one-dimensional and the permutation action of S_n, in the case 
               n=2.
%C A006950 Also the number of partitions of n in which all odd parts occur with 
               multiplicity 1. There is no restricton on the even parts. E.g a(9)=13 
               because "9=8+1=7+2=6+3=6+2+1=5+4=5+3+1=5+2+2=4+4+1=4+3+2=4+2+2+1= 
               3+2+2+2=2+2+2+2+1" - Noureddine Chair (n.chair(AT)rocketmail.com), 
               Feb 03 2005
%D A006950 A. Adem and R. J. Milgram, Cohomology of Finite Groups, Springer-Verlag, 
               2nd. ed., 2004; p. 108.
%D A006950 N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, 
               Academic Press, 1995 (includes this sequence).
%H A006950 N. Chair, <a href="http://arXiv.org/abs/hep-th/0409011">Partition identities 
               from Partial Supersymmetry</a>
%F A006950 a(n)=(1/n)*Sum_{k=1..n} (-1)^(k+1)*A002129(k)*a(n-k), n>1, a(0)=1. - 
               Vladeta Jovovic (vladeta(AT)eunet.rs), Feb 05 2002
%F A006950 G.f.: 1/Sum_{k>0} (-x)^(k*(k+1)/2). a(n) = A059777(n-1)+A059777(n), n>
               0. - Vladeta Jovovic (vladeta(AT)eunet.rs), Sep 22 2002
%F A006950 G.f.: Product (1+x^m)^(if A001511(m)>1, A001511(m)-1 else A001511(m)); 
               m=1..inf - Jon Perry (perry(AT)globalnet.co.uk), Apr 15 2005
%F A006950 Expansion of q*eta(q^16)/(eta(q^8)*eta(q^32)) in powers of q^8.
%F A006950 G.f.: 1/B(x) where B(x)= g.f. A106459. - Michael Somos Nov 02 2005
%F A006950 Expansion of 1/psi(-q) in powers of q where psi() is a Ramanujan theta 
               function.
%F A006950 G.f.: exp( Sum_{n>=1} [Sum_{d|n} (-1)^(n-d)*d] * x^n/n ). [From Paul 
               D. Hanna (pauldhanna(AT)juno.com), Jul 22 2009]
%o A006950 (PARI) {a(n)=polcoeff(exp(sum(m=1, n+1, sumdiv(m, d, (-1)^(m-d)*d)*x^m/
               m)+x*O(x^n)), n)} [From Paul D. Hanna (pauldhanna(AT)juno.com), Jul 
               22 2009]
%Y A006950 Cf. A015128, A046682.
%Y A006950 Cf. A163203. [From Paul D. Hanna (pauldhanna(AT)juno.com), Jul 22 2009]
%Y A006950 Sequence in context: A071682 A014670 A036034 this_sequence A106507 A052335 
               A160333
%Y A006950 Adjacent sequences: A006947 A006948 A006949 this_sequence A006951 A006952 
               A006953
%K A006950 nonn
%O A006950 0,4
%A A006950 N. J. A. Sloane (njas(AT)research.att.com), Warren D. Smith
%E A006950 G.f. and more terms from Vladeta Jovovic (vladeta(AT)eunet.rs), Feb 05 
               2002

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