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A262064 Expansion of f(x^9, x^15) / f(-x^2, -x^4) in powers of x where f(, ) is the Ramanujan general theta function 2
1, 0, 1, 0, 2, 0, 3, 0, 5, 1, 7, 1, 11, 2, 15, 4, 22, 6, 30, 9, 42, 14, 56, 20, 77, 29, 101, 41, 135, 57, 176, 78, 231, 107, 297, 143, 385, 191, 490, 253, 627, 332, 793, 432, 1003, 561, 1257, 721, 1578, 924, 1963, 1177, 2443, 1492, 3022, 1882, 3734, 2367, 4589 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,5

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..2500

Michael Somos, Introduction to Ramanujan theta functions

Eric Weisstein's World of Mathematics, Ramanujan Theta Functions

FORMULA

Euler transform of period 48 sequence [ 0, 1, 0, 1, 0, 1, 0, 1, 1, 1, 0, 1, 0, 1, 1, 1, 0, 0, 0, 1, 0, 1, 0, 0, 0, 1, 0, 1, 0, 0, 0, 1, 1, 1, 0, 1, 0, 1, 1, 1, 0, 1, 0, 1, 0, 1, 0, 0, ...].

a(n) = A143067(2*n).

EXAMPLE

G.f. = 1 + x^2 + 2*x^4 + 3*x^6 + 5*x^8 + x^9 + 7*x^10 + x^11 + 11*x^12 + ...

G.f. = q^5 + q^101 + 2*q^197 + 3*q^293 + 5*q^389 + q^437 + 7*q^485 + q^533 + ...

MATHEMATICA

a[ n_] := SeriesCoefficient[ QPochhammer[ -x^9, x^24] QPochhammer[ -x^15, x^24] QPochhammer[ x^24] / QPochhammer[ x^2], {x, 0, n}];

PROG

(PARI) {a(n) = if( n<0, 0, A = x * O(x^n); polcoeff( subst( prod(k=1, n\3, 1 - x^k * [1, 0, 0, 1, 0, 1, 0, 0][k%8 + 1], 1 + x * O(x^(n\3))), x, -x^3) / eta(x^2 + x * O(x^n)), n))};

CROSSREFS

Cf. A143067.

Sequence in context: A079977 A227093 A266772 * A008799 A325346 A325836

Adjacent sequences:  A262061 A262062 A262063 * A262065 A262066 A262067

KEYWORD

nonn

AUTHOR

Michael Somos, Sep 10 2015

STATUS

approved

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Last modified May 16 19:46 EDT 2021. Contains 343951 sequences. (Running on oeis4.)