OFFSET
1,2
COMMENTS
LINKS
Vaclav Kotesovec, Table of n, a(n) for n = 1..1000
Michael Somos, Introduction to Ramanujan theta functions
Eric Weisstein's World of Mathematics, Ramanujan Theta Functions
FORMULA
Expansion of eta(q^2)^11 * eta(q^4)^2 / eta(q)^6 in powers of q.
Euler transform of period 4 sequence [ 6, -5, 6, -7, ...].
EXAMPLE
G.f. = q + 6*q^2 + 16*q^3 + 32*q^4 + 60*q^5 + 92*q^6 + 128*q^7 + 192*q^8 + ...
MATHEMATICA
a[ n_] := SeriesCoefficient[ EllipticTheta[ 3, 0, q]^3 EllipticTheta[ 2, 0, q]^4 / 16, {q, 0, n}];
a[ n_] := SeriesCoefficient[ q QPochhammer[ q^2]^11 QPochhammer[ q^4]^2 / QPochhammer[ q]^6, {q, 0, n}];
nmax = 50; CoefficientList[Series[Product[(1-x^k)^7 * (1+x^(2*k))^2 * (1+x^k)^13, {k, 1, nmax}], {x, 0, nmax}], x] (* Vaclav Kotesovec, Jul 11 2016 *)
PROG
(PARI) {a(n) = local(A); if( n<1, 0, n--; A = x * O(x^n); polcoeff( eta(x^2 + A)^11 * eta(x^4 + A)^2 / eta(x + A)^6, n))};
(Magma) Basis( ModularForms( Gamma0(4), 7/2), 50) [2] ;
CROSSREFS
KEYWORD
nonn
AUTHOR
Michael Somos, Jun 10 2014
STATUS
approved