A086660 Stirling transform of Hermite numbers: Sum_{k=0..n} Stirling2(n,k) * HermiteH(k,0).

1, 0, -2, -6, -2, 90, 598, 1554, -10082, -164310, -1101242, -1496286, 64767118, 965876730, 7104497398, 57428274, -856472198402, -14195316779190, -122409183339482, 25272908324034, 21770258523698158

Offset: 0

Author

Vladeta Jovovic, Sep 12 2003

Keywords

• sign

Links

• G. C. Greubel, Table of n, a(n) for n = 0..500

Crossrefs

Cf. A067994, A052859.

Programs

Magma

m:=50; R:=PowerSeriesRing(Rationals(), m); b:=Coefficients(R!(Exp(-(Exp(x)-1)^2))); [Factorial(n-1)*b[n]: n in [1..m]]; // G. C. Greubel, Jul 12 2018

Mathematica

Table[Sum[StirlingS2[n,k]HermiteH[k,0],{k,0,n}],{n,0,20}] (* Harvey P. Dale, Mar 24 2013 *)
With[{nmax = 50}, CoefficientList[Series[Exp[-(Exp[x] - 1)^2], {x, 0, nmax}], x]*Range[0, nmax]!] (* G. C. Greubel, Jul 12 2018 *)

PARI

x='x+O('x^50); Vec(serlaplace(exp(-(exp(x)-1)^2))) \\ G. C. Greubel, Jul 12 2018

Formula

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