A081020 Even order Taylor coefficients at x = 0 of exp(-x^2/(x^2-2)), odd order coefficients being equal to zero.

1, 1, 9, 195, 7665, 473445, 42110145, 5085535455, 799363389825, 158394573362025, 38590445989920825, 11330437552124766075, 3943491069629507821425, 1604701708312172643298125, 754577935727586683368280625, 405920422302165926006881404375

Offset

0,3

Links

Table of n, a(n) for n=0..15.

Formula

E.g.f.: exp(-x^2/(x^2-2)) (even orders only).

a(n) ~ 2^n * n^(2*n - 1/4) / exp(2*n - 2*sqrt(n) + 1/2). - Vaclav Kotesovec, Sep 27 2021

Maple

a:= n-> (2*n)!*coeff(series(exp(-x^2/(x^2-2)), x, 2*n+1), x, 2*n):
seq(a(n), n=0..16);  # Alois P. Heinz, Sep 27 2021

Mathematica

terms = 12;
m = 2*terms+2;
Partition[CoefficientList[Exp[-x^2/(x^2-2)] + O[x]^(m+2), x]*Range[0, m]!, 2][[2 ;; , 1]] (* Jean-François Alcover, Sep 27 2021 *)

Prog

(PARI) my(x='x+O('x^35)); select(x->(x!=0), Vec(serlaplace(exp(-x^2/(x^2-2))))) \\ Michel Marcus, Sep 27 2021

Crossrefs

Sequence in context: A266485 A279132 A334777 * A358740 A017426 A244506

Adjacent sequences: A081017 A081018 A081019 * A081021 A081022 A081023

Keyword

nonn

Author

Karol A. Penson, Mar 01 2003

Extensions

a(0)=1 prepended by Alois P. Heinz, Sep 27 2021

Status

approved