A159522 Numerator of Hermite(n, 3/16).

1, 3, -119, -1125, 42321, 702963, -24976551, -614805237, 20534573985, 691164284643, -21582336376791, -949437293473413, 27539617738101489, 1540954535989466835, -41203060308232477191, -2884999709417821999893, 70454876663552890207041

Offset: 0

Author

N. J. A. Sloane, Nov 12 2009

Keywords

• sign
• frac

Links

• G. C. Greubel, Table of n, a(n) for n = 0..450

Crossrefs

Cf. A159521.

Programs

Magma

[Numerator((&+[(-1)^k*Factorial(n)*(3/8)^(n-2*k)/( Factorial(k) *Factorial(n-2*k)): k in [0..Floor(n/2)]])): n in [0..30]]; // G. C. Greubel, Jun 09 2018

Mathematica

Numerator[Table[HermiteH[n,3/16],{n,0,50}]] (* Vladimir Joseph Stephan Orlovsky, Apr 29 2011 *)

PARI

a(n)=numerator(polhermite(n,3/16)) \\ Charles R Greathouse IV, Jan 29 2016

Formula

From G. C. Greubel, Jun 09 2018: (Start)

a(n) = 16^n * Hermite(n,3/16).

E.g.f.: exp(6*x-252*x^2).

a(n) = Sum_{k=0..floor(n/2)} (-1)^k*n!*(3/8)^(n-2k)/(k!*(n-2k)!). (End)