A160224 Numerator of Hermite(n, 1/29).

1, 2, -1678, -10084, 8447020, 84739192, -70869959816, -996927845296, 832429051182992, 15079519188668960, -12571151938430794976, -278779816630273497152, 232033893531586021651648, 6090959605928612309819264, -5061471196749802724815296640

Offset: 0

Author

N. J. A. Sloane, Nov 12 2009

Keywords

• sign
• frac

Examples

			Numerators of 1, 2/29, -1678/841, -10084/24389, 8447020/707281..
		

Links

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

Crossrefs

Cf. A009973 (denominators).

Programs

Magma

[Numerator((&+[(-1)^k*Factorial(n)*(2/29)^(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

Mathematica

Table[29^n*HermiteH[n, 2/29], {n, 0, 30}] (* G. C. Greubel, Sep 26 2018 *)

PARI

a(n)=numerator(polhermite(n, 1/29)) \\ Charles R Greathouse IV, Jan 29 2016

PARI

x='x+O('x^30); Vec(serlaplace(exp(2*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, 1/29).

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

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