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A213617 Expansion of psi(x) * f(-x^3)^3 in powers of x where psi() and f() are Ramanujan theta functions. 5
1, 2, 3, 3, 3, 5, 4, 5, 4, 5, 7, 5, 8, 4, 5, 8, 8, 9, 5, 7, 9, 6, 9, 9, 7, 10, 10, 11, 5, 6, 12, 12, 10, 10, 7, 10, 12, 14, 10, 5, 15, 8, 13, 8, 12, 17, 10, 16, 7, 9, 14, 12, 15, 11, 11, 12, 12, 16, 14, 15, 13, 15, 13, 7, 12, 17, 16, 15, 10, 13, 18, 16, 20 (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

G. C. Greubel, Table of n, a(n) for n = 0..1000

M. Somos, Introduction to Ramanujan theta functions

Eric Weisstein's World of Mathematics, Ramanujan Theta Functions

FORMULA

Expansion of q^(-11/24) * eta(q^2)^2 * eta(q^3)^3 / eta(q)^2 in powers of q.

Euler transform of period 6 sequence [ 2, 0, -1, 0, 2, -3, ...].

6 * a(n) = A213618(24*n + 11).

EXAMPLE

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

G.f. = q^11 + 2*q^35 + 3*q^59 + 3*q^83 + 3*q^107 + 5*q^131 + 4*q^155 + 5*q^179 + ...

MATHEMATICA

a[ n_] := SeriesCoefficient[ QPochhammer[ x^2]^2 QPochhammer[ x^3]^3 / QPochhammer[x]^2, {x, 0, n}]; (* Michael Somos, Apr 26 2015 *)

PROG

(PARI) {a(n) = my(A); if( n<0, 0, A = x * O(x^n); polcoeff( eta(x^2 + A)^2 * eta(x^3 + A)^3 / eta(x + A)^2, n))};

CROSSREFS

Cf. A213618.

Sequence in context: A092308 A326576 A205394 * A205778 A328972 A081831

Adjacent sequences:  A213614 A213615 A213616 * A213618 A213619 A213620

KEYWORD

nonn

AUTHOR

Michael Somos, Jun 16 2012

STATUS

approved

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Last modified January 21 05:39 EST 2020. Contains 331104 sequences. (Running on oeis4.)