A294181 -id:A294181 - cp's OEIS frontend

A294182 Coefficients in expansion of E_4/E_6.

1, 744, 393768, 210962976, 112966533672, 60492691156464, 32393330061359904, 17346357971979746880, 9288829947058862457384, 4974090926254339741926216, 2663584184830281769743846768, 1426327104764356980195826984032

Offset: 0

Seiichi Manyama, Feb 11 2018

nonn

Seiichi Manyama, Table of n, a(n) for n = 0..366

Cf. A000706, A004009 (E_4), A013973 (E_6), A288261.

E_k/E_{k+2}: A294181 (k=2), this sequence (k=4), A294183 (k=6).

terms = 12;
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}];
E4[x]/E6[x] + O[x]^terms // CoefficientList[#, x]& (* Jean-François Alcover, Feb 23 2018 *)

Convolution inverse of A288261.

a(n) ~ 8 * Gamma(3/4)^8 * exp(2*Pi*n) / (3*Pi^2). - Vaclav Kotesovec, Jun 03 2018

A294183 Coefficients in expansion of E_6/E_8.

Original entry on oeis.org

1, -984, 393768, -129252576, 38684099112, -10970838627984, 3003345011096352, -801909012374388672, 210169391033048138280, -54295810529811041175672, 13867098270790394508774768, -3508693915623201191415922848

Offset: 0

Seiichi Manyama, Feb 11 2018

sign

Seiichi Manyama, Table of n, a(n) for n = 0..421

Cf. A008410 (E_8). A013973 (E_6), A287933, A288840.

E_k/E_{k+2}: A294181 (k=2), A294182 (k=4), this sequence (k=6).

terms = 12;
E6[x_] = 1 - 504*Sum[k^5*x^k/(1 - x^k), {k, 1, terms}];
E8[x_] = 1 + 480*Sum[k^7*x^k/(1 - x^k), {k, 1, terms}];
E6[x]/E8[x] + O[x]^terms // CoefficientList[#, x]& (* Jean-François Alcover, Feb 23 2018 *)

Convolution inverse of A288840.

a(n) ~ (-1)^n * 512 * Pi^12 * exp(Pi*sqrt(3)*n) * n / (3 * Gamma(1/3)^18). - Vaclav Kotesovec, Jun 03 2018

cp's OEIS Frontend

A294182 Coefficients in expansion of E_4/E_6.

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