A144141 a(n) = Hermite(n,2).

1, 4, 14, 40, 76, -16, -824, -3104, -880, 46144, 200416, -121216, -4894016, -16666880, 60576896, 708980224, 1018614016, -18612911104, -109084520960, 233726715904, 5080118660096, 10971406004224, -169479359707136, -1160659303014400, 3153413334470656

Offset: 0

Author

Vladimir Joseph Stephan Orlovsky, Sep 11 2008

Keywords

• sign

Links

• G. C. Greubel, Table of n, a(n) for n = 0..729

Crossrefs

Cf. A000898, A000321, A062267.

Programs

Magma

[(&+[(-1)^k*Factorial(n)*(4)^(n-2*k)/( Factorial(k) *Factorial(n-2*k)): k in [0..Floor(n/2)]]): n in [0..30]]; // G. C. Greubel, Jul 10 2018

Mathematica

lst={};Do[AppendTo[lst,HermiteH[n,2]],{n,0,7^2}];lst
HermiteH[Range[0,30],2]  (* Harvey P. Dale, May 20 2012 *)

PARI

for(n=0, 50, print1(polhermite(n, 2), ", " )) \\ G. C. Greubel, Jul 10 2018

Formula

From G. C. Greubel, Jul 10 2018: (Start)

E.g.f.: exp(4*x - x^2).

a(n) = Sum_{k=0..floor(n/2)} (-1)^k*n!*4^(n-2*k)/(k!*(n-2*k)!). (End)