login
The OEIS Foundation is supported by donations from users of the OEIS and by a grant from the Simons Foundation.

 

Logo


Hints
(Greetings from The On-Line Encyclopedia of Integer Sequences!)
A240948 Expansion of chi(x^5)^6 + x * chi(x)^6 in powers of x where chi() is a Ramanujan theta function. 1
1, 1, 6, 15, 26, 57, 102, 172, 276, 453, 743, 1128, 1698, 2539, 3780, 5531, 7882, 11238, 15918, 22259, 30861, 42438, 58110, 78909, 106392, 142872, 190698, 253179, 334266, 439581, 575956, 750613, 974316, 1260336, 1624702, 2086806, 2670162, 3406695, 4333590 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,3

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) * chi(x^5))^6 - 4 * x * chi(x) * chi(x^5) in powers of x where chi() is a Ramanujan theta function.

Expansion of (eta(q^2)^2 / (eta(q) * eta(q^4)))^6 + (eta(q^10)^2 / (eta(q^5) * eta(q^20)))^6 in powers of q.

G.f. is a period 1 Fourier series which satisfies f(-1 / (320 t)) = f(t) where q = exp(2 Pi i t).

a(n) ~ exp(Pi*sqrt(n)) / (2^(3/2) * n^(3/4)). - Vaclav Kotesovec, Nov 29 2019

EXAMPLE

G.f. = 1 + x + 6*x^2 + 15*x^3 + 26*x^4 + 57*x^5 + 102*x^6 + 172*x^7 + ...

G.f. = q^-5 + q^-1 + 6*q^3 + 15*q^7 + 26*q^11 + 57*q^15 + 102*q^19 + ...

MATHEMATICA

a[ n_] := SeriesCoefficient[ QPochhammer[ x^5, -x^5]^-6 + x QPochhammer[ x, -x]^-6, {x, 0, n}];

nmax = 40; CoefficientList[Series[x*Product[((1 + x^k)/(1 + x^(2*k)))^6, {k, 1, nmax}] + Product[((1 + x^(5*k))/(1 + x^(10*k)))^6, {k, 1, nmax}], {x, 0, nmax}], x] (* Vaclav Kotesovec, Nov 29 2019 *)

PROG

(PARI) {a(n) = local(A); if( n<0, 0, A = x * O(x^n); polcoeff( x * (eta(x^2 + A)^2 / (eta(x + A) * eta(x^4 + A)))^6 + (eta(x^10 + A)^2 / (eta(x^5 + A) * eta(x^20 + A)))^6, n))};

(PARI) {a(n) = local(A); if( n<0, 0, A = x * O(x^n); A = eta(x^2 + A)^2 * eta(x^10 + A)^2 / (eta(x + A) * eta(x^4 + A) * eta(x^5 + A) * eta(x^20 + A)); polcoeff( A^5 - 4 * x * A, n))};

CROSSREFS

Sequence in context: A284629 A022601 A112150 * A072257 A227952 A316320

Adjacent sequences:  A240945 A240946 A240947 * A240949 A240950 A240951

KEYWORD

nonn

AUTHOR

Michael Somos, Aug 04 2014

STATUS

approved

Lookup | Welcome | Wiki | Register | Music | Plot 2 | Demos | Index | Browse | More | WebCam
Contribute new seq. or comment | Format | Style Sheet | Transforms | Superseeker | Recent
The OEIS Community | Maintained by The OEIS Foundation Inc.

License Agreements, Terms of Use, Privacy Policy. .

Last modified May 13 17:46 EDT 2021. Contains 343864 sequences. (Running on oeis4.)