OFFSET
0,20
COMMENTS
Michael Somos found a four term identity: eta(q) * eta(q^30) * eta(q^35) * eta(q^42) + eta(q^3) * eta(q^10) * eta(q^14) * eta(q^105) = eta(q^2) * eta(q^15) * eta(q^21) * eta(q^70) + eta(q^5) * eta(q^6) * eta(q^7) * eta(q^210).
LINKS
Seiichi Manyama, Table of n, a(n) for n = 0..10000
Michael Somos, A Remarkable eta-product Identity
MATHEMATICA
eta[q_] := q^(1/24)*QPochhammer[q]; CoefficientList[Series[q^(-1/2) *eta[q^3]*eta[q^10]*eta[q^14]*eta[q^105] + q^(-1/2)*eta[q]*eta[q^30] *eta[q^35]*eta[q^42], {q, 0, 50}], q] (* G. C. Greubel, Jul 29 2018 *)
PROG
(PARI) q='q+O('q^50); A = q*eta(q^3)*eta(q^10)*eta(q^14)*eta(q^105); B = eta(q)*eta(q^30)*eta(q^35)*eta(q^42); concat(vector(4), Vec(A + B)) \\ G. C. Greubel, Jul 29 2018
CROSSREFS
KEYWORD
sign
AUTHOR
Seiichi Manyama, May 03 2017
STATUS
approved