A160263 Numerator of Hermite(n, 14/29).

1, 28, -898, -119336, 1189900, 836209808, 13406815624, -8063638544864, -383633726413168, 97762575920121280, 8544799476205933024, -1405112141642673804928, -197439019874757039348032, 22832490910422530976921856, 4956511354073268289737879680

Offset: 0

Author

N. J. A. Sloane, Nov 12 2009

Keywords

• sign
• frac

Examples

			Numerators of 1, 28/29, -898/841, -119336/24389, 1189900/707281, ...
		

Links

• G. C. Greubel, Table of n, a(n) for n = 0..372

Crossrefs

Cf. A009973 (denominators).

Programs

Magma

[Numerator((&+[(-1)^k*Factorial(n)*(28/29)^(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

Maple

seq(coeff(series(factorial(n)*exp(28*x-841*x^2),x,n+1), x, n), n = 0..15); # Muniru A Asiru, Sep 28 2018

Mathematica

Table[29^n*HermiteH[n, 14/29], {n, 0, 30}] (* G. C. Greubel, Sep 26 2018 *)

PARI

a(n)=numerator(polhermite(n, 14/29)) \\ Charles R Greathouse IV, Jan 29 2016

PARI

x='x+O('x^30); Vec(serlaplace(exp(28*x - 841*x^2))) \\ G. C. Greubel, Sep 26 2018

Formula

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

a(n) = 29^n * Hermite(n, 14/29).

E.g.f.: exp(28*x - 841*x^2).

a(n) = numerator(Sum_{k=0..floor(n/2)} (-1)^k*n!*(28/29)^(n-2*k)/(k!*(n-2*k)!)). (End)