0,6

McKay-Thompson series of class 72e for the Monster group.

Also number of partitions of n into odd parts in which no part appears more than twice, cf. A070048 and A096938. - Vladeta Jovovic (vladeta(AT)eunet.rs), Jan 18 2005

Also number of partitions of n into distinct parts congruent to 1 or 2 modulo 3. (Follows from second G.F.) - Naoki Sato (nsato7(AT)yahoo.ca), Jul 20 2005

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

D. Ford, J. McKay and S. P. Norton, More on replicable functions, Commun. Algebra 22, No. 13, 5175-5193 (1994).

R. Zumkeller, Table of n, a(n) for n = 0..200

Index entries for McKay-Thompson series for Monster simple group

Eric Weisstein's World of Mathematics, Link to a section of The World of Mathematics.

N. Chair, Partition identities from Partial Supersymmetry

G.f.: 1/Product_{k>=0} (1-x^(6*k+1))*(1-x^(6*k+5)) = Product_{k>=0} (1+x^(3*k+1))*(1+x^(3*k+2)) = 1/Product_{k>=0} (1-x^k+x^(2*k)). - Vladeta Jovovic (vladeta(AT)eunet.rs), Jun 08 2003

Expansion of q^(1/12)eta(q^2)eta(q^3)/(eta(q)eta(q^6)) in powers of q.

Euler transform of period 6 sequence [1, 0, 0, 0, 1, 0, ...]. - Michael Somos, Jan 09 2005

Given g.f. A(x), then B(x)=(A(x^12)/x)^4 satisfies 0=f(B(x), B(x^2)) where f(u, v)=uv^4+(1-u^3)v^3+6u^2v^2+(u^4-u)v+u^3 - Michael Somos, Jan 09 2005

T72e = 1/q + q^11 + q^23 + q^35 + q^47 + 2q^59 + 2q^71 + 3q^83 + ...

(PARI) {a(n)=local(A); if(n<0, 0, A=x*O(x^n); polcoeff( eta(x^2+A)*eta(x^3+A)/eta(x+A)/eta(x^6+A), n))} /* Michael Somos Jan 09 2005 */

Cf. A001651, A000726, A132462, A132463.

Sequence in context: A125059 A029112 A029094 this_sequence A081166 A036846 A058740

Adjacent sequences: A003102 A003103 A003104 this_sequence A003106 A003107 A003108

nonn

N. J. A. Sloane (njas(AT)research.att.com), Herman P. Robinson

More terms from Vladeta Jovovic (vladeta(AT)eunet.rs), Jun 08 2003