A160194 Numerator of Hermite(n, 9/28).

1, 9, -311, -9855, 277041, 17946009, -381486279, -45642389679, 636016842465, 148858685615529, -904139249676759, -591663300859964511, -1426321263133495791, 2770347275877071597625, 32201658639821938929561, -14913850922254971477399951, -323570411102447744202418239

Offset: 0

Author

N. J. A. Sloane, Nov 12 2009

Keywords

• sign
• frac

Examples

			Numerators of 1, 9/14, -311/196, -9855/2744, 277041/38416, ...
		

Links

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

Crossrefs

Cf. A001023 (denominators).

Programs

Magma

[Numerator((&+[(-1)^k*Factorial(n)*(9/14)^(n-2*k)/( Factorial(k) *Factorial(n-2*k)): k in [0..Floor(n/2)]])): n in [0..30]]; // G. C. Greubel, Jul 12 2018

Mathematica

Numerator[Table[HermiteH[n, 9/28], {n, 0, 30}]] (* or *) Table[14^n* HermiteH[n, 9/28], {n,0,30}] (* G. C. Greubel, Jul 12 2018 *)

PARI

a(n)=numerator(polhermite(n, 9/28)) \\ Charles R Greathouse IV, Jan 29 2016

Formula

From G. C. Greubel, Jul 12 2018: (Start)

a(n) = 14^n * Hermite(n, 9/28).

E.g.f.: exp(9*x - 196*x^2).

a(n) = numerator(Sum_{k=0..floor(n/2)} (-1)^k*n!*(9/14)^(n-2*k)/(k!*(n-2*k)!)). (End)