A293120 Expansion of e.g.f. exp(x^2/(1+x)).

1, 0, 2, -6, 36, -240, 1920, -17640, 183120, -2116800, 26943840, -374220000, 5628934080, -91122071040, 1579034096640, -29155689763200, 571308920582400, -11838533804697600, 258608278645516800, -5938673374272038400, 143003892952893772800

Offset: 0

Author

Seiichi Manyama, Sep 30 2017

Keywords

• sign

Links

• Seiichi Manyama, Table of n, a(n) for n = 0..444

Crossrefs

Column k=1 of A293133.

Cf. A111884, A293121.

Cf. A052845.

Programs

Mathematica

CoefficientList[Series[E^(x^2/(1+x)), {x, 0, 20}], x] * Range[0, 20]! (* Vaclav Kotesovec, Sep 30 2017 *)

PARI

x='x+O('x^66); Vec(serlaplace(exp(x^2/(1+x))))

Formula

E.g.f.: exp(x^2/(1+x)).

a(n) = (-1)^n * A052845(n).

a(n) ~ (-1)^n * n^(n-1/4) * exp(-3/2 + 2*sqrt(n) - n)/sqrt(2). - Vaclav Kotesovec, Sep 30 2017