A289396 -id:A289396 - cp's OEIS frontend

A289416 Coefficients of (q*(j(q)-1728))^(-1/24) where j(q) is the elliptic modular invariant.

1, 41, 12809, 4767210, 1969719570, 861799083811, 391094324350380, 182038077972154741, 86322373755372340110, 41521193849940130872000, 20197774625594843441436930, 9915082544034345319047507780

Offset: 0

Seiichi Manyama, Jul 06 2017

nonn

Seiichi Manyama, Table of n, a(n) for n = 0..367

(q*(j(q)-1728))^(k/24): A289563 (k=-96), A289562 (k=-72), A289561 (k=-48), A289417 (k=-24), this sequence (k=-1), A106203 (k=1), A289330 (k=2), A289331 (k=3), A289332 (k=4), A289333 (k=5), A289334 (k=6), A007242 (k=12), A289063 (k=24).

CoefficientList[Series[((256/QPochhammer[-1, x]^8 + x*QPochhammer[-1, x]^16/256)^3 - 1728*x)^(-1/24), {x, 0, 20}], x] (* Vaclav Kotesovec, Mar 07 2018 *)

G.f.: Product_{n>=1} (1-q^n)^(-A289061(n)/24) = Product_{n>=1} (1-q^n)^(1-A289396(n)).

a(n) ~ c * exp(2*Pi*n) / n^(11/12), where c = Gamma(3/4)^(1/3) * exp(Pi/12) / (2^(1/12) * 3^(1/6) * Pi^(1/12) * Gamma(1/12)) = 0.086380262154841817375196725... - Vaclav Kotesovec, Mar 07 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).

A289395 a(n) = A110163(n)/8.

Original entry on oeis.org

-30, 3345, -512030, 88617345, -16360095774, 3146109187345, -622294742016030, 125653141164729345, -25774484801870336030, 5353054537005702294801, -1122995842254699148800030, 237552033786848383463977345, -50601782105721473281984512030

Offset: 1

Seiichi Manyama, Jul 05 2017

sign

Seiichi Manyama, Table of n, a(n) for n = 1..424

Cf. A004009 (E_4), A108091 (E_4^(1/8)), A110163.

Cf. A289394, A289396.

a(n) = 1 + (1/(24*n)) * Sum_{d|n} A008683(n/d) * A288261(d).

cp's OEIS Frontend

A289416 Coefficients of (q*(j(q)-1728))^(-1/24) where j(q) is the elliptic modular invariant.

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

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Formula

A289395 a(n) = A110163(n)/8.

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