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

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

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

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]

Sequence in context: A071682 A014670 A036034 this_sequence A106507 A052335 A160333

Adjacent sequences: A006947 A006948 A006949 this_sequence A006951 A006952 A006953

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