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

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

Offset

0,2

Comments

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)).

Links

Table of n, a(n) for n=0..13.

Formula

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

Mathematica

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

Crossrefs

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.

Sequence in context: A157851 A278011 A282012 * A147883 A166964 A316337

Adjacent sequences: A378466 A378467 A378468 * A378470 A378471 A378472

Keyword

sign

Author

Vaclav Kotesovec, Nov 27 2024

Status

approved