A160280 Numerator of Hermite(n, 18/29).

1, 36, -386, -135000, -2912244, 803439216, 53415783816, -6185340350496, -851589691267440, 52572710870646336, 14783982337749774816, -352049632685279478144, -286207027989716394858816, -3197683221510109228058880, 6143086278048774757772750976

Offset: 0

Author

N. J. A. Sloane, Nov 12 2009

Keywords

• sign
• frac

Examples

			Numerators of 1, 36/29, -386/841, -135000/24389, -2912244/707281, ...
		

Links

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

Crossrefs

Cf. A009973 (denominators).

Programs

Magma

[Numerator((&+[(-1)^k*Factorial(n)*(36/29)^(n-2*k)/( Factorial(k) *Factorial(n-2*k)): k in [0..Floor(n/2)]])): n in [0..30]]; // G. C. Greubel, Oct 03 2018

Mathematica

Table[29^n*HermiteH[n, 18/29], {n, 0, 30}] (* G. C. Greubel, Oct 03 2018 *)

PARI

a(n)=numerator(polhermite(n, 18/29)) \\ Charles R Greathouse IV, Jan 29 2016

PARI

x='x+O('x^30); Vec(serlaplace(exp(36*x - 841*x^2))) \\ G. C. Greubel, Oct 03 2018

Formula

From G. C. Greubel, Oct 03 2018: (Start)

a(n) = 29^n * Hermite(n, 18/29).

E.g.f.: exp(36*x - 841*x^2).

a(n) = numerator(Sum_{k=0..floor(n/2)} (-1)^k*n!*(36/29)^(n-2*k)/(k!*(n-2*k)!)). (End)