A160223 Numerator of Hermite(n, 27/28).

1, 27, 337, -12069, -722175, -574533, 1399950609, 39149968059, -2784415333503, -197953513837605, 4478672422983249, 896901929663959323, 4904316613023132033, -4086610128587640090501, -135330870931832163283695, 18773382870529500408009723

Offset: 0

Author

N. J. A. Sloane, Nov 12 2009

Keywords

• sign
• frac

Examples

			Numerators of 1, 27/14, 337/196, -12069/2744, -722175/38416
		

Links

• G. C. Greubel, Table of n, a(n) for n = 0..417

Crossrefs

Cf. A001023 (denominators).

Programs

Magma

[Numerator((&+[(-1)^k*Factorial(n)*(27/14)^(n-2*k)/( Factorial(k) *Factorial(n-2*k)): k in [0..Floor(n/2)]])): n in [0..30]]; // G. C. Greubel, Sep 26 2018

Mathematica

Table[14^n*HermiteH[n, 27/28], {n, 0, 30}] (* G. C. Greubel, Sep 26 2018 *)

PARI

a(n)=numerator(polhermite(n, 27/28)) \\ Charles R Greathouse IV, Jan 29 2016

PARI

x='x+O('x^30); Vec(serlaplace(exp(27*x - 196*x^2))) \\ G. C. Greubel, Sep 26 2018

Formula

From G. C. Greubel, Sep 26 2018: (Start)

a(n) = 14^n * Hermite(n, 27/28).

E.g.f.: exp(27*x - 196*x^2).

a(n) = numerator(Sum_{k=0..floor(n/2)} (-1)^k*n!*(27/14)^(n-2*k)/(k!*(n-2*k)!)). (End)