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A232635
Expansion of psi(x) * phi(x^2)^2 in powers of x where phi(), psi() are Ramanujan theta functions.
1
1, 1, 4, 5, 4, 8, 1, 4, 8, 4, 13, 12, 4, 8, 8, 1, 12, 8, 8, 12, 16, 13, 4, 16, 4, 12, 20, 8, 5, 12, 12, 12, 16, 8, 8, 20, 17, 16, 16, 8, 20, 24, 8, 8, 16, 1, 24, 16, 8, 12, 20, 16, 12, 28, 12, 33, 20, 8, 16, 12, 16, 20, 24, 8, 16, 32, 1, 12, 32, 8, 16, 32, 8
OFFSET
0,3
COMMENTS
Ramanujan theta functions: f(q) (see A121373), phi(q) (A000122), psi(q) (A010054), chi(q) (A000700).
Theta function of cubic lattice with respect to point (1/4, 0, 0).
LINKS
Eric Weisstein's World of Mathematics, Ramanujan Theta Functions
FORMULA
Expansion of q^(-1/8) * eta(q^4)^10 / (eta(q) * eta(q^2)^2 * eta(q^8)^4) in powers of q.
Euler transform of period 8 sequence [ 1, 3, 1, -7, 1, 3, 1, -3, ...].
a(3*n + 2) = 4 * A213023(n).
EXAMPLE
G.f. = 1 + x + 4*x^2 + 5*x^3 + 4*x^4 + 8*x^5 + x^6 + 4*x^7 + 8*x^8 + 4*x^9 + ...
G.f. = q + q^9 + 4*q^17 + 5*q^25 + 4*q^33 + 8*q^41 + q^49 + 4*q^57 + 8*q^65 + ...
MATHEMATICA
a[ n_] := SeriesCoefficient[ QPochhammer[ q^4]^10 / (QPochhammer[ q] QPochhammer[ q^2]^2 QPochhammer[ q^8]^4), {q, 0, n}]
PROG
(PARI) {a(n) = local(A); if( n<0, 0, A = x * O(x^n); polcoeff( eta(x^4 + A)^10 / (eta(x + A) * eta(x^2 + A)^2 * eta(x^8 + A)^4), n))}
CROSSREFS
Cf. A213023.
Sequence in context: A200623 A248671 A343442 * A201296 A350089 A246954
KEYWORD
nonn
AUTHOR
Michael Somos, Nov 27 2013
STATUS
approved