A233431 Expansion of q * f(-q^7)^3 * f(-q^2, -q^5) / f(-x^3, -q^4)^2 in powers of q where f() is a Ramanujan theta function.

1, 0, -1, 2, 2, -3, 1, 3, -2, -1, 3, 0, 0, 0, 1, 2, -1, -2, 2, 0, -1, 3, 0, -1, 4, 0, -3, 2, 2, -4, -1, 4, 2, -3, 2, 2, 0, -1, 0, 2, 0, -3, 2, 4, -2, 1, 2, -3, 1, 2, -4, 0, 3, -2, 3, 3, 1, 0, -1, 0, 2, -3, -2, 5, 0, -1, 3, 0, -3, -1, 2, 0, -1, 1, 4, 0, 3, 0

Offset

1,4

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 = 1..1000

Michael Somos, Introduction to Ramanujan theta functions

Eric Weisstein's World of Mathematics, Ramanujan Theta Functions

Formula

Euler transform of period 7 sequence [ 0, -1, 2, 2, -1, 0, -2, ...].

Example

G.f. = q - q^3 + 2*q^4 + 2*q^5 - 3*q^6 + q^7 + 3*q^8 - 2*q^9 - q^10 + ...

Mathematica

a[ n_] := SeriesCoefficient[ q Product[ (1 - q^k)^{0, 1, -2, -2, 1, 0, 2, 2}[[Mod[k, 7, 1]]], {k, n}], {q, 0, n}]

Prog

(PARI) {a(n) = local(A); if( n<1, 0, n--; A = x * O(x^n); polcoeff( prod( k=1, n, (1 - x^k + A)^[ 2, 0, 1, -2, -2, 1, 0, 2][k%7 + 1]), n))}
(Sage) ModularForms( Gamma1(7), 1, prec=70).1
(Magma) Basis( ModularForms( Gamma1(7), 1), 70) [2]

Crossrefs

Sequence in context: A339461 A190263 A144911 * A160650 A304092 A339669

Adjacent sequences: A233428 A233429 A233430 * A233432 A233433 A233434

Keyword

sign

Author

Michael Somos, Dec 09 2013

Status

approved