A160219 Numerator of Hermite(n, 17/28).

1, 17, -103, -15079, -135215, 21345217, 627890089, -39529818871, -2394937325023, 83251577454065, 9864615699400249, -158647716730130567, -45233234080226093327, -22686119865309399391, 230122896835121911804745, 4036590672017890484538473

Offset: 0

Author

N. J. A. Sloane, Nov 12 2009

Keywords

• sign
• frac

Examples

			Numerators of 1, 17/14, -103/196, -15079/2744, -135215/38416
		

Links

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

Crossrefs

Cf. A001023 (denominators)

Programs

Magma

[Numerator((&+[(-1)^k*Factorial(n)*(17/14)^(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

Numerator[Table[HermiteH[n, 17/28], {n, 0, 50}]] (* G. C. Greubel, Sep 26 2018 *)

PARI

a(n)=numerator(polhermite(n, 17/28)) \\ Charles R Greathouse IV, Jan 29 2016

PARI

x='x+O('x^30); Vec(serlaplace(exp(17*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, 17/28).

E.g.f.: exp(17*x - 196*x^2).

a(n) = numerator(Sum_{k=0..floor(n/2)} (-1)^k*n!*(17/14)^(n-2*k)/(k!*(n-2*k)!)). (End)