login
This site is supported by donations to The OEIS Foundation.

 

Logo


Hints
(Greetings from The On-Line Encyclopedia of Integer Sequences!)
A282099 Coefficients in q-expansion of (E_2^2*E_4 - 2*E_2*E_6 + E_4^2)/1728, where E_2, E_4, E_6 are the Eisenstein series shown in A006352, A004009, A013973, respectively. 7
0, 1, 36, 252, 1168, 3150, 9072, 16856, 37440, 61317, 113400, 161172, 294336, 371462, 606816, 793800, 1198336, 1420146, 2207412, 2476460, 3679200, 4247712, 5802192, 6436872, 9434880, 9844375, 13372632, 14900760, 19687808, 20511990, 28576800, 28630112, 38347776 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,3

COMMENTS

Multiplicative because A001158 is. - Andrew Howroyd, Jul 25 2018

LINKS

Seiichi Manyama, Table of n, a(n) for n = 0..1000

FORMULA

G.f.: phi_{5, 2}(x) where phi_{r, s}(x) = Sum_{n, m>0} m^r * n^s * x^{m*n}.

a(n) = (A282208(n) - 2*A282096(n) + A008410(n))/1728. - Seiichi Manyama, Feb 19 2017

a(n) = n^2*A001158(n) for n > 0. - Seiichi Manyama, Feb 19 2017

EXAMPLE

a(6) = 1^5*6^2 + 2^5*3^2 + 3^5*2^2 + 6^5*1^2 = 9072.

MATHEMATICA

a[0]=0; a[n_]:=(n^2)*DivisorSigma[3, n]; Table[a[n], {n, 0, 32}] (* Indranil Ghosh, Feb 21 2017 *)

PROG

(PARI) a(n) = if (n==0, 0, n^2*sigma(n, 3)); \\ Michel Marcus, Feb 21 2017

CROSSREFS

Cf. A282097 (phi_{3, 2}), this sequence (phi_{5, 2}).

Cf. A006352 (E_2), A004009 (E_4), A013973 (E_6), A282208 (E_2^2*E_4), A282096 (E_2*E_6), A008410 (E_8 = E_4^2).

Cf. A001158 (sigma_3(n)), A281372 (n*sigma_3(n)), this sequence (n^2*sigma_3(n)), A282213 (n^3*sigma_3(n)).

Sequence in context: A219888 A233363 A030165 * A247840 A017342 A115332

Adjacent sequences:  A282096 A282097 A282098 * A282100 A282101 A282102

KEYWORD

nonn,mult

AUTHOR

Seiichi Manyama, Feb 06 2017

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 19 10:32 EDT 2019. Contains 324219 sequences. (Running on oeis4.)