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A281371 Coefficients in q-expansion of (E_2*E_4 - E_6)^2/518400, where E_2, E_4, E_6 are the Eisenstein series shown in A006352, A004009, A013973, respectively. 3
0, 0, 1, 36, 492, 3608, 18828, 74760, 250352, 717984, 1866558, 4365580, 9635472, 19639032, 38559416, 71222616, 128258496, 219619968, 370366101, 597550068, 955638824, 1471571136, 2253173892, 3335433368, 4932972864, 7064391840, 10133162774, 14128072488, 19743952032, 26864847352 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,4

COMMENTS

This is (up to a constant factor), the numerator of the expression phi defined in Cohn (2017) (see phi on page 114 of the Notices version).

LINKS

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

Cohn, Henry. A conceptual breakthrough in sphere packing, arXiv preprint arXiv:1611.01685 (2016); also Notices Amer. Math. Soc., 64:2 (2017), pp. 102-115.

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)^2/518400, q, M+1);

seriestolist(t1);

MATHEMATICA

terms = 30;

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

E4[x_] = 1 + 240*Sum[k^3*x^k/(1 - x^k), {k, 1, terms}];

E6[x_] = 1 - 504*Sum[k^5*x^k/(1 - x^k), {k, 1, terms}];

(E2[x]*E4[x] - E6[x])^2/518400 + O[x]^terms // CoefficientList[#, x]& (* Jean-Fran├žois Alcover, Feb 27 2018 *)

CROSSREFS

Cf. A006352, A004009, A013973, A145094, A281372 (the square root).

Sequence in context: A104671 A323549 A128986 * A090408 A268635 A233101

Adjacent sequences:  A281368 A281369 A281370 * A281372 A281373 A281374

KEYWORD

nonn

AUTHOR

N. J. A. Sloane, Feb 04 2017

STATUS

approved

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Last modified January 15 10:38 EST 2021. Contains 340187 sequences. (Running on oeis4.)