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A255319 Expansion of psi(x^3) * f(x, x^5) in powers of x where psi(), f() are Ramanujan theta functions. 7
1, 1, 0, 1, 1, 1, 0, 0, 2, 1, 1, 1, 0, 0, 1, 0, 1, 1, 1, 2, 0, 1, 0, 1, 1, 1, 1, 0, 0, 0, 2, 1, 0, 1, 1, 1, 1, 0, 1, 1, 1, 0, 1, 1, 0, 1, 2, 0, 0, 1, 1, 2, 0, 1, 0, 0, 1, 0, 1, 1, 0, 1, 0, 2, 1, 2, 1, 0, 2, 0, 1, 1, 0, 0, 2, 0, 0, 0, 1, 1, 0, 0, 0, 1, 2, 3, 1 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,9

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 chi(x) * f(-x^6) * f(-x^12) in powers of x where chi(), f() are Ramanujan theta functions.

Expansion of q^(-17/24) * eta(q^2)^2 * eta(q^6) * eta(q^12) / (eta(q) * eta(q^4)) in powers of q.

Euler transform of period 12 sequence [ 1, -1, 1, 0, 1, -2, 1, 0, 1, -1, 1, -2, ...].

EXAMPLE

G.f. = 1 + x + x^3 + x^4 + x^5 + 2*x^8 + x^9 + x^10 + x^11 + x^14 + x^16 + ...

G.f. = q^17 + q^41 + q^89 + q^113 + q^137 + 2*q^209 + q^233 + q^257 + q^281 + ...

MATHEMATICA

a[ n_] := SeriesCoefficient[ QPochhammer[ x^6] QPochhammer[ x^12]  QPochhammer[ -x, x^2], {x, 0, n}];

PROG

(PARI) {a(n) = my(A); if( n<0, 0, A = x * O(x^n); polcoeff( eta(x^2 + A)^2 * eta(x^6 + A) * eta(x^12 + A) / (eta(x + A) * eta(x^4 + A)), n))};

CROSSREFS

Sequence in context: A262097 A085975 A277778 * A214088 A005091 A276516

Adjacent sequences:  A255316 A255317 A255318 * A255320 A255321 A255322

KEYWORD

nonn

AUTHOR

Michael Somos, Feb 21 2015

STATUS

approved

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Last modified June 20 12:57 EDT 2021. Contains 345164 sequences. (Running on oeis4.)