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!)
A282097 Coefficients in q-expansion of (3*E_2*E_4 - 2*E_6 - E_2^3)/1728, where E_2, E_4, E_6 are the Eisenstein series shown in A006352, A004009, A013973, respectively. 9
0, 1, 12, 36, 112, 150, 432, 392, 960, 1053, 1800, 1452, 4032, 2366, 4704, 5400, 7936, 5202, 12636, 7220, 16800, 14112, 17424, 12696, 34560, 19375, 28392, 29160, 43904, 25230, 64800, 30752, 64512, 52272, 62424, 58800, 117936, 52022, 86640, 85176, 144000, 70602 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,3

COMMENTS

Multiplicative because A000203 is. - Andrew Howroyd, Jul 25 2018

LINKS

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

FORMULA

a(n) = (3*A282019(n) - 2*A013973(n) - A282018(n))/1728.

G.f.: phi_{3, 2}(x) where phi_{r, s}(x) = Sum_{n, m>0} m^r * n^s * x^{m*n}.

a(n) = n^2*A000203(n) for n > 0. - Seiichi Manyama, Feb 19 2017

G.f.: Sum_{k>=1} k^3*x^k*(1 + x^k)/(1 - x^k)^3. - Ilya Gutkovskiy, May 02 2018

EXAMPLE

a(6) = 1^3*6^2 + 2^3*3^2 + 3^3*2^2 + 6^3*1^2 = 432.

MATHEMATICA

a[0]=0; a[n_]:=(n^2)*DivisorSigma[1, n]; Table[a[n], {n, 0, 41}] (* Indranil Ghosh, Feb 21 2017 *)

terms = 42; Ei[n_] = 1-(2n/BernoulliB[n]) Sum[k^(n-1) x^k/(1-x^k), {k, terms}]; CoefficientList[(3*Ei[2]*Ei[4] - 2*Ei[6] - Ei[2]^3)/1728 + O[x]^terms, x] (* Jean-Fran├žois Alcover, Mar 01 2018 *)

PROG

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

(MAGMA) [0] cat [n^2*DivisorSigma(1, n): n in [1..50]]; // Vincenzo Librandi, Mar 01 2018

CROSSREFS

Cf. this sequence (phi_{3, 2}), A282099 (phi_{5, 2}).

Cf. A006352 (E_2), A004009 (E_4), A013973 (E_6), A282018 (E_2^3), A282019 (E_2*E_4).

Cf. A000203 (sigma(n)), A064987 (n*sigma(n)), this sequence (n^2*sigma(n)), A282211 (n^3*sigma(n)).

Sequence in context: A172212 A060621 A058880 * A055551 A073403 A191817

Adjacent sequences:  A282094 A282095 A282096 * A282098 A282099 A282100

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 March 31 03:48 EDT 2020. Contains 333136 sequences. (Running on oeis4.)