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A224822 Expansion of phi(-q) * phi(-q^3)^2 in powers of q where phi() is a Ramanujan theta function. 3
1, -2, 0, -4, 10, 0, 4, -16, 0, -2, 8, 0, 12, -8, 0, -16, 26, 0, 0, -24, 0, -8, 8, 0, 20, -10, 0, -4, 32, 0, 8, -48, 0, -8, 16, 0, 10, -8, 0, -32, 40, 0, 8, -24, 0, 0, 16, 0, 28, -18, 0, -24, 40, 0, 4, -64, 0, -8, 8, 0, 32, -24, 0, -16, 58, 0, 16, -24, 0, -16 (list; graph; refs; listen; history; text; internal format)
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 eta(q)^2 * eta(q^3)^4 / (eta(q^2) * eta(q^6)^2) in powers of q.
Euler transform of period 6 sequence [-2, -1, -6, -1, -2, -3, ...].
G.f.: (Sum_{k in Z} (-1)^k * x^k^2) * (Sum_{k in Z} (-1)^k * x^(3*k^2))^2.
a(3*n + 2) = 0. a(2*n) = A028967(n). a(3*n) = A224821(n).
EXAMPLE
G.f. = 1 - 2*q - 4*q^3 + 10*q^4 + 4*q^6 - 16*q^7 - 2*q^9 + 8*q^10 + 12*q^12 +
...
MATHEMATICA
a[ n_] := SeriesCoefficient[ EllipticTheta[ 4, 0, q] EllipticTheta[ 4, 0, q^3]^2, {q, 0, n}];
PROG
(PARI) {a(n) = my(A); if( n<0, 0, A = x * O(x^n); polcoeff( eta(x + A)^2 * eta(x^3 + A)^4 / (eta(x^2 + A) * eta(x^6 + A)^2), n))};
CROSSREFS
Sequence in context: A077119 A002938 A111938 * A246928 A167341 A359188
KEYWORD
sign
AUTHOR
Michael Somos, Jul 20 2013
STATUS
approved

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Last modified February 22 02:45 EST 2024. Contains 370239 sequences. (Running on oeis4.)