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A226034 Expansion of f(-x)^6 / (chi(x) * phi(-x)^6) in powers of x where phi(), chi(), f() are Ramanujan theta functions. 1
1, 11, 73, 368, 1552, 5755, 19337, 60054, 174801, 481760, 1266992, 3198963, 7791921, 18382187, 42139440, 94126547, 205343040, 438390320, 917501570, 1885269635, 3808353889, 7571955531, 14833349529, 28657374307, 54646711136, 102932171227, 191644299945 (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

Vaclav Kotesovec, A method of finding the asymptotics of q-series based on the convolution of generating functions, arXiv:1509.08708 [math.CO], Sep 30 2015

M. Somos, Introduction to Ramanujan theta functions

Eric Weisstein's World of Mathematics, Ramanujan Theta Functions

FORMULA

Expansion of q^(-19/24) * eta(q^2)^4 * eta(q^3)^6 * eta(q^4) / eta(q)^11 in powers of q.

a(n) = 12 * A001935(9*n + 7).

a(n) ~ exp(3*Pi*sqrt(n/2)) / (2^(19/4) * 3^(5/2) * n^(3/4)). - Vaclav Kotesovec, Oct 14 2015

EXAMPLE

1 + 11*x + 73*x^2 + 368*x^3 + 1552*x^4 + 5755*x^5 + 19337*x^6 + 60054*x^7 + ...

q^19 + 11*q^43 + 73*q^67 + 368*q^91 + 1552*q^115 + 5755*q^139 + 19337*q^163 + ...

MATHEMATICA

nmax=60; CoefficientList[Series[Product[(1+x^k)^4 * (1-x^(3*k))^6 * (1-x^(4*k)) / (1-x^k)^7, {k, 1, nmax}], {x, 0, nmax}], x] (* Vaclav Kotesovec, Oct 14 2015 *)

eta[q_]:= q^(1/24)*QPochhammer[q]; a[n_]:= SeriesCoefficient[q^(-19/24)* eta[q^2]^4*eta[q^3]^6*eta[q^4]/eta[q]^11, {q, 0, n}]; Table[a[n], {n, 0, 50}] (* G. C. Greubel, Mar 15 2018 *)

PROG

(PARI) {a(n) = local(A); if( n<0, 0, A = x * O(x^n); polcoeff( eta(x^2 + A)^4 * eta(x^3 + A)^6 * eta(x^4 + A) / eta(x + A)^11, n))}

CROSSREFS

Cf. A001935.

Sequence in context: A197308 A142015 A123039 * A217946 A163775 A092244

Adjacent sequences:  A226031 A226032 A226033 * A226035 A226036 A226037

KEYWORD

nonn

AUTHOR

Michael Somos, May 28 2013

STATUS

approved

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Last modified January 19 01:11 EST 2021. Contains 340262 sequences. (Running on oeis4.)