A289395 -id:A289395 - cp's OEIS frontend

A289397 Coefficients in expansion of (q*j(q))^(-1/24).

1, -31, 3809, -620190, 111669570, -21246138749, 4186228503780, -845058129488699, 173647689528542310, -36170751826552656600, 7615730581866678419370, -1617501058117655447210580, 346019784662582818549094159

Offset: 0

Seiichi Manyama, Jul 05 2017

sign

Seiichi Manyama, Table of n, a(n) for n = 0..424

(q*j(q))^(k/24): this sequence (k=-1), A106205 (k=1), A289297 (k=2), A289298 (k=3), A289299 (k=4), A289300 (k=5), A289301 (k=6), A289302 (k=7), A007245 (k=8), A289303 (k=9), A289304 (k=10), A289305 (k=11), A161361 (k=12).

Cf. A000521 (j(q)), A066395.

(q*1728*KleinInvariantJ[-Log[q]*I/(2*Pi)])^(-1/24) + O[q]^13 // CoefficientList[#, q]& (* Jean-François Alcover, Nov 02 2017 *)

G.f.: Product_{n>=1} (1-q^n)^(-A192731(n)/24) = Product_{n>=1} (1-q^n)^(1-A289395(n)).
a(n) ~ (-1)^n * c * exp(Pi*sqrt(3)*n) / n^(7/8), where c = 0.13397834215417716857261649901051678539339753563926756586381... = 2^(1/8) * exp(Pi/(8 * sqrt(3))) * sqrt(Pi) / (3^(1/8) * Gamma(1/8) * Gamma(1/3)^(3/4)). - Vaclav Kotesovec, Mar 05 2018, updated Mar 06 2018
a(n) * A106205(n) ~ c * exp(2*Pi*sqrt(3)*n) / n^2, where c = -sqrt(2-sqrt(2)) / (16*Pi). - Vaclav Kotesovec, Mar 06 2018

A289394 a(n) = A288968(n)/4.

Original entry on oeis.org

6, 87, 1606, 32325, 694662, 15528631, 357084294, 8381837481, 199870549318, 4825613579415, 117685008900294, 2893968761750149, 71662670867210118, 1785128827454666007, 44695890712594405318, 1124087528135149982673, 28381310631267855206406

Offset: 1

Seiichi Manyama, Jul 05 2017

nonn

Seiichi Manyama, Table of n, a(n) for n = 1..702

Cf. A006352 (E_2), A288968, A289392 (E_2^(1/4)).

Cf. A289395, A289396.

a(n) = 1/2 + (1/(48*n)) * Sum_{d|n} A008683(n/d) * A288877(d).

A289396 a(n) = A288851(n)/12.

Original entry on oeis.org

42, 11949, 4265002, 1713048225, 733858320426, 327479221781677, 150310620492466218, 70428822653977730817, 33523597190772239402026, 16156445902957272648713901, 7865129058155349010009168938, 3860735065245250133098748713633

Offset: 1

Seiichi Manyama, Jul 05 2017

nonn

Seiichi Manyama, Table of n, a(n) for n = 1..367

Cf. A013973 (E_6), A109817 (E_6^(1/12)), A288851.

Cf. A289394, A289395.

a(n) = 1 + (1/(24*n)) * Sum_{d|n} A008683(n/d) * A288840(d).

cp's OEIS Frontend

A289397 Coefficients in expansion of (q*j(q))^(-1/24).

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A289394 a(n) = A288968(n)/4.

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Formula

A289396 a(n) = A288851(n)/12.

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