A243763 Expansion of q * phi(q)^3 * psi(q^2)^4 in powers of q where phi(), psi() are Ramanujan theta functions.

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

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

Sequence in context: A036488 A131949 A345023 * A061235 A239358 A171494

Adjacent sequences: A243760 A243761 A243762 * A243764 A243765 A243766

Keyword

nonn

Author

Michael Somos, Jun 10 2014

Status

approved