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!)
A185699 Expansion of (11 * E_2(x^11) - E_2(x)) / 2 in powers of x where E_2() is an Eisenstein series. 2
5, 12, 36, 48, 84, 72, 144, 96, 180, 156, 216, 12, 336, 168, 288, 288, 372, 216, 468, 240, 504, 384, 36, 288, 720, 372, 504, 480, 672, 360, 864, 384, 756, 48, 648, 576, 1092, 456, 720, 672, 1080, 504, 1152, 528, 84, 936, 864, 576, 1488, 684, 1116, 864, 1176, 648 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,1

COMMENTS

Ramanujan theta functions: f(q) (see A121373), phi(q) (A000122), psi(q) (A010054), chi(q) (A000700).

REFERENCES

B. C. Berndt, Ramanujan's Notebooks Part III, Springer-Verlag, see p. 480, Entry 8(i).

Carlos J. Moreno and Samuel S. Wagstaff, Jr., Sums of Squares of Integers, Chapman & Hall/CRC, Boca Raton, London, New York,  p. 246 (corrected).

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 5 * (phi(x) * phi(x^11))^2 - 20 * x * (f(x) * f(x^11))^2 + 32 * x^2 * (f(-x^2) * f(-x^22))^2 - 20 * x^3 * (psi(-x) * psi(-x^11))^2 in powers of x where f(), phi(), psi() are Ramanujan theta functions.

Expansion of 5 + 12*Sum_{n>=1} Chi0(n)*n*q^n / (1 - q^n), where Chi0(n) = 1 if gcd(n,11) = 1 and 0 otherwise. See the Moreno-Wagstaff reference p. 246, second equation multiplied by 12 (a misprint has been corrected, after mail exchange with C. J. Moreno). - Wolfdieter Lang, Jan 02 2017

EXAMPLE

G.f. = 5 + 12*x + 36*x^2 + 48*x^3 + 84*x^4 + 72*x^5 + 144*x^6 + 96*x^7 + ...

MATHEMATICA

terms = 54;

E2[x_] = 1 - 24*Sum[k*x^k/(1 - x^k), {k, 1, terms}];

(11*E2[x^11] - E2[x])/2 + O[x]^terms // CoefficientList[#, x]& (* Jean-Fran├žois Alcover, Feb 27 2018 *)

PROG

(PARI) {a(n) = if( n<1, 5 * (n==0), 12 * (sigma( n) - if( n%11, 0, 11 * sigma( n / 11))))};

CROSSREFS

Cf. A006352, A006571, A272196.

Sequence in context: A032281 A294654 A229043 * A301873 A077918 A300534

Adjacent sequences:  A185696 A185697 A185698 * A185700 A185701 A185702

KEYWORD

nonn,easy

AUTHOR

Michael Somos, Feb 10 2011

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 June 23 07:38 EDT 2021. Contains 345395 sequences. (Running on oeis4.)