A081021 Even order Taylor coefficients at x = 0 of exp( (sqrt(2)-sqrt(-2*x^2+2))/(-2*x^2+2)^(1/2) ), odd order coefficients being equal to zero.

1, 12, 375, 22155, 2113020, 295956045, 57148456365, 14541025999500, 4712328126180675, 1894168782984052575, 924528651354021413700, 538492713580088225984025

Offset

1,2

Links

G. C. Greubel, Table of n, a(n) for n = 1..224

Formula

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

From Vaclav Kotesovec, May 05 2024: (Start)

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

a(n) = 3*(2*n - 3)*(2*n - 1)*a(n-1) - (2*n - 3)*(2*n - 1)*(12*n^2 - 48*n + 47)*a(n-2) + 4*(n-3)*(n-2)*(2*n - 5)^2*(2*n - 3)*(2*n - 1)*a(n-3). (End)

Mathematica

Rest[With[{nmax = 100}, CoefficientList[Series[Exp[(Sqrt[2] - Sqrt[2 - 2*x^2])/(Sqrt[2 - 2*x^2]) ], {x, 0, nmax}], x]*Range[0, nmax]!][[1 ;; -1 ;; 2]]] (* G. C. Greubel, Sep 11 2018 *)

Crossrefs

Cf. A081020.

Sequence in context: A235685 A024298 A177112 * A269609 A251590 A352651

Adjacent sequences: A081018 A081019 A081020 * A081022 A081023 A081024

Keyword

nonn

Author

Karol A. Penson, Mar 01 2003

Status

approved