A246837 Expansion of phi(x) * psi(x) * psi(x^4) in powers of x where phi(), psi() are Ramanujan theta functions.

1, 3, 2, 1, 5, 5, 3, 5, 4, 4, 6, 6, 3, 5, 9, 6, 10, 4, 3, 13, 4, 5, 9, 8, 5, 8, 12, 4, 13, 10, 7, 14, 5, 5, 11, 8, 9, 12, 6, 7, 15, 15, 6, 13, 12, 6, 13, 6, 7, 21, 17, 6, 13, 8, 10, 12, 14, 9, 8, 15, 6, 22, 8, 9, 22, 14, 10, 11, 15, 11, 22, 16, 6, 8, 14, 11

Offset

0,2

Comments

Ramanujan theta functions: f(q) (see A121373), phi(q) (A000122), psi(q) (A010054), chi(q) (A000700).

Links

G. C. Greubel, Table of n, a(n) for n = 0..1000

Michael Somos, Introduction to Ramanujan theta functions

Eric Weisstein's World of Mathematics, Ramanujan Theta Functions

Formula

Expansion of q^(-5/8) * eta(q^2)^7 * eta(q^8)^2 / (eta(q)^3 * eta(q^4)^3) in powers of q.

Euler transform of period 8 sequence [3, -4, 3, -1, 3, -4, 3, -3, ...].

Example

G.f. = 1 + 3*x + 2*x^2 + x^3 + 5*x^4 + 5*x^5 + 3*x^6 + 5*x^7 + 4*x^8 + ...
G.f. = q^5 + 3*q^13 + 2*q^21 + q^29 + 5*q^37 + 5*q^45 + 3*q^53 + 5*q^61 + ...

Mathematica

eta[q_] := q^(1/24)*QPochhammer[q]; a:= CoefficientList[Series[q^(-5/8)* eta[q^2]^7*eta[q^8]^2/(eta[q]^3*eta[q^4]^3), {q, 0, 60}], q]]; Table[ a[[n]], {n, 1, 50}] (* G. C. Greubel, Aug 05 2018 *)

Prog

(PARI) {a(n) = my(A); if( n<0, 0, A = x * O(x^n); polcoeff( eta(x^2 + A)^7 * eta(x^8 + A)^2 / (eta(x + A)^3 * eta(x^4 + A)^3), n))};

Crossrefs

Sequence in context: A068389 A091597 A091595 * A132969 A132970 A192022

Adjacent sequences: A246834 A246835 A246836 * A246838 A246839 A246840

Keyword

nonn

Author

Michael Somos, Sep 04 2014

Status

approved