A160236 Numerator of Hermite(n, 5/29).

1, 10, -1582, -49460, 7488172, 407648600, -58899040520, -4702980076400, 646447502318480, 69747774931223200, -9088444540784918240, -1264042019751023406400, 155513980696092323212480, 27068563933615579666902400, -3129783062564598942695063680

Offset: 0

Author

N. J. A. Sloane, Nov 12 2009

Keywords

• sign
• frac

Examples

			Numerators of 1, 10/29, -1582/841, -49460/24389, 7488172/707281
		

Links

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

Crossrefs

Cf. A009973 (denominators).

Programs

Magma

[Numerator((&+[(-1)^k*Factorial(n)*(10/29)^(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

Numerator[HermiteH[Range[0,20],5/29]] (* Harvey P. Dale, Mar 10 2013 *)
Table[29^n*HermiteH[n, 5/29], {n, 0, 30}] (* G. C. Greubel, Sep 26 2018 *)

PARI

a(n)=numerator(polhermite(n, 5/29)) \\ Charles R Greathouse IV, Jan 29 2016

PARI

x='x+O('x^30); Vec(serlaplace(exp(10*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, 5/29).

E.g.f.: exp(10*x - 841*x^2).

a(n) = numerator(Sum_{k=0..floor(n/2)} (-1)^k*n!*(10/29)^(n-2*k)/(k!*(n-2*k)!)). (End)