A289566 - OEIS

A289566

Coefficients in expansion of 1/E_4^(1/2).

1, -120, 20520, -3934560, 793510440, -164694615120, 34824089129760, -7460017581785280, 1613575314347164200, -351613291994820018840, 77073167391611232305520, -16975579813113940564868640, 3753822590560913900129106720

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OFFSET

0,2

LINKS

Seiichi Manyama, Table of n, a(n) for n = 0..423

FORMULA

G.f.: Product_{n>=1} (1-q^n)^(-A110163(n)/2).

a(n) ~ (-1)^n * c * exp(Pi*sqrt(3)*n) / sqrt(n), where c = 3^(7/2) * Gamma(2/3)^9 / (2^(9/2) * Pi^(7/2)) = 0.5756695813762774104492155417156662666189119445257965... - Vaclav Kotesovec, Jul 09 2017, updated Mar 05 2018

MATHEMATICA

nmax = 20; CoefficientList[Series[(1 + 240*Sum[DivisorSigma[3, k]*x^k, {k, 1, nmax}])^(-1/2), {x, 0, nmax}], x] (* Vaclav Kotesovec, Jul 09 2017 *)

CROSSREFS

1/E_k^(1/2): A289565 (k=2), this sequence (k=4), A289567 (k=6), A001943 (k=8), A289568 (k=10), A289569 (k=14).

Cf. A001943 (1/E_4), A110163, A289292 (E_4^(1/2)).

Sequence in context: A229605 A268474 A363516 * A229693 A105188 A264957

Adjacent sequences: A289563 A289564 A289565 * A289567 A289568 A289569

KEYWORD

sign

AUTHOR

Seiichi Manyama, Jul 08 2017

STATUS

approved