A160195 Numerator of Hermite(n, 11/28).

1, 11, -271, -11605, 191041, 20298091, -151161359, -49403884981, -128655965695, 153515367677771, 2142567291427441, -578212001091160469, -15599082172637890751, 2548319349233802047915, 107524435593334513794161, -12802407797068425987221749

Offset: 0

Author

N. J. A. Sloane, Nov 12 2009

Keywords

• sign
• frac

Examples

			Numerators of 1, 11/14, -271/196, -11605/2744, 191041/38416, ...
		

Links

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

Crossrefs

Cf. A001023 (denominators).

Programs

Magma

[Numerator((&+[(-1)^k*Factorial(n)*(11/14)^(n-2*k)/( Factorial(k) *Factorial(n-2*k)): k in [0..Floor(n/2)]])): n in [0..30]]; // G. C. Greubel, Sep 24 2018

Mathematica

Table[14^n*HermiteH[n, 11/28], {n, 0, 30}] (* G. C. Greubel, Sep 24 2018 *)

PARI

a(n)=numerator(polhermite(n, 11/28)) \\ Charles R Greathouse IV, Jan 29 2016

PARI

x='x+O('x^30); Vec(serlaplace(exp(11*x - 196*x^2))) \\ G. C. Greubel, Sep 24 2018

Formula

From G. C. Greubel, Sep 24 2018: (Start)

a(n) = 14^n * Hermite(n, 11/28).

E.g.f.: exp(11*x - 196*x^2).

a(n) = numerator(Sum_{k=0..floor(n/2)} (-1)^k*n!*(11/14)^(n-2*k)/(k!*(n-2*k)!)). (End)