0,4

Number of partitions of n in which each even part occurs with even multiplicity. There is no restriction on the odd parts.

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

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

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.

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

N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, Academic Press, 1995 (includes this sequence).

A. Adem and R. J. Milgram, Cohomology of Finite Groups, Springer-Verlag, 2nd. ed., 2004; p. 108.

N. Chair, Partition identities from Partial Supersymmetry

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

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

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

Expansion of q*eta(q^16)/(eta(q^8)*eta(q^32)) in powers of q^8.

G.f.: 1/B(x) where B(x)= g.f. A106459. - Michael Somos Nov 02 2005

Expansion of 1/psi(-q) in powers of q where psi() is a Ramanujan theta function.

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]

(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]

Cf. A015128, A046682.

Cf. A163203. [From Paul D. Hanna (pauldhanna(AT)juno.com), Jul 22 2009]

Adjacent sequences: A006947 A006948 A006949 this_sequence A006951 A006952 A006953

Sequence in context: A071682 A014670 A036034 this_sequence A106507 A052335 A160333

nonn

N. J. A. Sloane (njas(AT)research.att.com), Warren D. Smith

G.f. and more terms from Vladeta Jovovic (vladeta(AT)eunet.rs), Feb 05 2002