A160246 Numerator of Hermite(n, 7/29).

1, 14, -1486, -67900, 6547756, 548499784, -47387630984, -6198886653904, 471157554050960, 90008424571645664, -5872265109220393184, -1596153412824165573056, 86302501271257396667584, 33424995502240561479908480, -1419140555765946374814673024

Offset: 0

Author

N. J. A. Sloane, Nov 12 2009

Keywords

• sign
• frac

Examples

			Numerators of 1, 14/29, -1486/841, -67900/24389, 6547756/707281,...
		

Links

• G. C. Greubel, Table of n, a(n) for n = 0..371

Crossrefs

Cf. A009973 (denominators)

Programs

Magma

[Numerator((&+[(-1)^k*Factorial(n)*(14/29)^(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, 7/29], {n, 0, 30}] (* G. C. Greubel, Sep 26 2018 *)

PARI

a(n)=numerator(polhermite(n, 7/29)) \\ Charles R Greathouse IV, Jan 29 2016

PARI

x='x+O('x^30); Vec(serlaplace(exp(14*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, 7/29).

E.g.f.: exp(14*x - 841*x^2).

a(n) = numerator(Sum_{k=0..floor(n/2)} (-1)^k*n!*(14/29)^(n-2*k)/(k!*(n-2*k)!)). (End)