login
The OEIS is supported by the many generous donors to the OEIS Foundation.

 

Logo

Year-end appeal: Please make a donation to the OEIS Foundation to support ongoing development and maintenance of the OEIS. We are now in our 59th year, we have over 358,000 sequences, and we’ve crossed 10,300 citations (which often say “discovered thanks to the OEIS”).

Other ways to Give
Hints
(Greetings from The On-Line Encyclopedia of Integer Sequences!)
A235870 Expansion of ( f(-q)^12 + 22 * q * f(-q)^6 * f(-q^5)^6 + 125 * q^2 * f(-q^5)^12 ) / (f(-q) * f(-q^5))^2 in powers of q where f() is a Ramanujan theta function. 1
1, 12, 72, 264, 696, 1380, 2304, 3192, 5400, 6924, 12600, 12384, 18912, 20184, 28512, 39000, 43032, 45432, 63144, 63600, 101640, 88944, 110304, 112104, 151200, 174540, 183024, 188400, 231936, 225000, 351360, 274704, 346392, 344448, 407952, 479400, 509592 (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

Michael Somos, Introduction to Ramanujan theta functions

Eric Weisstein's World of Mathematics, Ramanujan Theta Functions

FORMULA

Expansion of ( ( (f(-q) * f(-q^5))^4 + 9*q * (f(-q) * f(-q^3) * f(-q^5) * f(-q^15))^2 + 27*q * (f(-q^3) * f(-q^15))^4 ) / (f(-q) * f(-q^3) * f(-q^5) * f(-q^15)) )^2 in powers of q where f() is a Ramanujan theta function.

G.f. is a period 1 Fourier series which satisfies f(-1 / (5 t)) = 25 (t/i)^4 f(t) where q = exp(2 Pi i t).

Convolution square of A028887.

EXAMPLE

G.f. = 1 + 12*q + 72*q^2 + 264*q^3 + 696*q^4 + 1380*q^5 + 2304*q^6 + ...

PROG

(PARI) {a(n) = my(A, u1, u5); if( n<0, 0, A = x * O(x^n); u1 = eta(x + A); u5 = eta(x^5 + A); polcoeff( ( u1^12 + 22*x * (u1 * u5)^6 + 125*x^2 * u5^12 ) / (u1 * u5)^2, n))};

(PARI) {a(n) = my(A, v1, v3); if( n<0, 0, A = x * O(x^n); v1 = eta(x + A) * eta(x^5 + A) ; v3 = eta(x^3 + A) * eta(x^15 + A) ; polcoeff( ( v1^4 + 9*x * (v1 * v3)^2 + 27*x^2 * v3^4 )^2 / (v1 * v3)^2, n))};

(Sage) A = ModularForms( Gamma0(5), 4, prec=36) . basis(); A[1] + 12/13 * (3*A[0] + 10*A[2]); # Michael Somos, Jun 13 2014

(Magma) A := Basis( ModularForms( Gamma0(5), 4), 36); A[1] + 12*A[2] + 72*A[3]; /* Michael Somos, Jun 13 2014 */

CROSSREFS

Cf. A028887.

Sequence in context: A188660 A047928 A300847 * A008533 A010024 A008414

Adjacent sequences: A235867 A235868 A235869 * A235871 A235872 A235873

KEYWORD

nonn

AUTHOR

Michael Somos, Jun 13 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 | Recents
The OEIS Community | Maintained by The OEIS Foundation Inc.

License Agreements, Terms of Use, Privacy Policy. .

Last modified December 7 14:20 EST 2022. Contains 358656 sequences. (Running on oeis4.)