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A281372 Coefficients in q-expansion of (E_2*E_4 - E_6)/720, where E_2, E_4, E_6 are the Eisenstein series shown in A006352, A004009, A013973, respectively. 12
0, 1, 18, 84, 292, 630, 1512, 2408, 4680, 6813, 11340, 14652, 24528, 28574, 43344, 52920, 74896, 83538, 122634, 130340, 183960, 202272, 263736, 279864, 393120, 393775, 514332, 551880, 703136, 707310, 952560, 923552, 1198368, 1230768, 1503684, 1517040, 1989396, 1874198, 2346120, 2400216, 2948400 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,3

COMMENTS

The q-expansion of the square of this expression is given in A281371.

Multiplicative because A001158 is. - Andrew Howroyd, Jul 23 2018

LINKS

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

FORMULA

a(n) = A145094(n)/240 for n > 0. - Seiichi Manyama, Feb 04 2017

G.f.: phi_{4, 1}(x) where phi_{r, s}(x) = Sum_{n, m>0} m^r * n^s * x^{m*n}. - Seiichi Manyama, Feb 04 2017

a(n) = n*A001158(n) for n > 0. - Seiichi Manyama, Feb 18 2017

G.f.: x*f'(x), where f(x) = Sum_{k>=1} k^3*x^k/(1 - x^k). - Ilya Gutkovskiy, Aug 31 2017

MAPLE

with(numtheory); M:=100;

E := proc(k) local n, t1; global M;

t1 := 1-(2*k/bernoulli(k))*add(sigma[k-1](n)*q^n, n=1..M+1);

series(t1, q, M+1); end;

e2:=E(2); e4:=E(4); e6:=E(6);

t1:=series((e2*e4-e6)/720, q, M+1);

seriestolist(t1);

MATHEMATICA

Table[If[n==0, 0, n * DivisorSigma[3, n]], {n, 0, 40}] (* Indranil Ghosh, Mar 11 2017 *)

terms = 41; Ei[n_] = 1-(2n/BernoulliB[n]) Sum[k^(n-1) x^k/(1-x^k), {k, terms}]; CoefficientList[(Ei[2] Ei[4] - Ei[6])/720 + O[x]^terms, x] (* Jean-Fran├žois Alcover, Mar 01 2018 *)

PROG

(PARI) for(n=0, 40, print1(if(n==0, 0, n * sigma(n, 3)), ", ")) \\ Indranil Ghosh, Mar 11 2017

(MAGMA) [0] cat [n*DivisorSigma(3, n): n in [1..50]]; // Vincenzo Librandi, Mar 01 2018

CROSSREFS

Cf. A001158, A006352, A004009, A013973, A145094, A281371.

Sequence in context: A039358 A043961 A067984 * A124935 A126405 A250101

Adjacent sequences:  A281369 A281370 A281371 * A281373 A281374 A281375

KEYWORD

nonn,mult

AUTHOR

N. J. A. Sloane, Feb 04 2017

STATUS

approved

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Last modified April 7 13:55 EDT 2020. Contains 333305 sequences. (Running on oeis4.)