A378468 -id:A378468 - cp's OEIS frontend

A378469 Coefficients in expansion of (1/E_4)^4.

1, -960, 567360, -266138880, 108735481920, -40500351480960, 14114830665358080, -4678563821426250240, 1491145606587529742400, -460511820740945555286720, 138585483759128030100927360, -40812342463218781348220286720, 11800049457060387849887324117760, -3358272262154871467174772417214080

Offset: 0

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Vaclav Kotesovec, Nov 27 2024

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In general, for k > 0, the expansion of 1/(E_4)^k is asymptotic to (-1)^n * k * 2^(9*k) * Pi^(12*k) * n^(k-1) * exp(Pi*sqrt(3)*n) / (3^(2*k) * Gamma(1/3)^(18*k) * Gamma(k+1)).

Cf. A001943 (k=1), A287933 (k=2), A378468 (k=3).
Cf. A289566 (k=1/2), A295815 (k=1/4), A289247 (k=1/8).
Cf. A004009, A289319.

nmax = 20; CoefficientList[Series[(1+240*Sum[DivisorSigma[3, k]*x^k, {k, 1, nmax}])^(-4), {x, 0, nmax}], x]

a(n) ~ (-1)^n * 34359738368 * Pi^48 * n^3 * exp(Pi*sqrt(3)*n) / (19683 * Gamma(1/3)^72).

cp's OEIS Frontend

A378469 Coefficients in expansion of (1/E_4)^4.

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