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A246837
Expansion of phi(x) * psi(x) * psi(x^4) in powers of x where phi(), psi() are Ramanujan theta functions.
2
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
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
KEYWORD
nonn
AUTHOR
Michael Somos, Sep 04 2014
STATUS
approved