A081022 Even order Taylor coefficients at x = 0 of exp( -(-2^(1/3)+(-3*x^2+2)^(1/3))/(-3*x^2+2)^(1/3) ), odd order coefficients being equal to zero.

1, 15, 615, 48825, 6351345, 1225996695, 328803049575, 116905182419025, 53200767201206625, 30152208510970120575, 20822956658564943457575, 17211467743309469796791625

Offset

1,2

Links

Table of n, a(n) for n=1..12.

Formula

In Maple notation: a(n)=subs(x=0, diff(exp(-(-2^(1/3)+(-3*x^2+2)^(1/3))/(-3*x^2+2)^(1/3)), x$2*n)), n=1, 2...

From Vaclav Kotesovec, May 05 2024: (Start)

a(n) ~ 2^(n - 1/2) * 3^(n + 1/8) * exp(4*n^(1/4)/3^(3/4) - 2*n - 1) * n^(2*n - 3/8).

a(n) = 12*(n-2)*(2*n - 1)*a(n-1) - 2*(2*n - 3)*(2*n - 1)*(27*n^2 - 135*n + 172)*a(n-2) + (2*n - 5)*(2*n - 3)*(2*n - 1)*(108*n^3 - 972*n^2 + 2928*n - 2951)*a(n-3) - 9*(n-4)*(n-3)*(2*n - 7)*(2*n - 5)*(2*n - 3)*(2*n - 1)*(3*n - 11)*(3*n - 10)*a(n-4). (End)

Mathematica

nmax = 20; Table[(CoefficientList[Series[E^(-1 + 1/(1 - 3*x^2/2)^(1/3)), {x, 0, 2*nmax}], x] * Range[0, 2*nmax]!)[[k]], {k, 3, 2*nmax, 2}] (* Vaclav Kotesovec, May 05 2024 *)

Crossrefs

Cf. A081020, A081021.

Sequence in context: A027505 A012210 A203172 * A049291 A351180 A092958

Adjacent sequences: A081019 A081020 A081021 * A081023 A081024 A081025

Keyword

nonn

Author

Karol A. Penson, Mar 01 2003

Status

approved