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A243763
Expansion of q * phi(q)^3 * psi(q^2)^4 in powers of q where phi(), psi() are Ramanujan theta functions.
1
1, 6, 16, 32, 60, 92, 128, 192, 253, 316, 432, 512, 604, 792, 896, 1024, 1272, 1410, 1584, 1920, 2104, 2236, 2688, 2944, 3101, 3732, 3904, 4096, 4884, 5080, 5376, 6144, 6424, 6776, 7776, 8096, 8188, 9492, 9856, 10112, 11664, 11704, 11952, 13824, 14100, 14360
OFFSET
1,2
COMMENTS
Ramanujan theta functions: f(q) (see A121373), phi(q) (A000122), psi(q) (A010054), chi(q) (A000700).
LINKS
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
Sequence in context: A036488 A131949 A345023 * A061235 A239358 A171494
KEYWORD
nonn
AUTHOR
Michael Somos, Jun 10 2014
STATUS
approved