A160292 Numerator of Hermite(n, 7/30).

1, 7, -401, -9107, 477601, 19735807, -936451601, -59841840107, 2530929662401, 233147132022007, -8618235208570001, -1109489740559021507, 34893836098508354401, 6235501451708274618607, -160480431014315950915601, -40407022162862341753633307, 800393754206596276404873601

Offset: 0

Author

N. J. A. Sloane, Nov 12 2009

Keywords

• sign
• frac

Examples

			Numerators of 1, 7/15, -401/225, -9107/3375, 477601/50625, ...
		

Links

• G. C. Greubel, Table of n, a(n) for n = 0..412

Crossrefs

Cf. A001024 (denominators).

Programs

Magma

[Numerator((&+[(-1)^k*Factorial(n)*(7/15)^(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[15^n*HermiteH[n, 7/30], {n, 0, 30}] (* G. C. Greubel, Oct 03 2018 *)

PARI

a(n)=numerator(polhermite(n, 7/30)) \\ Charles R Greathouse IV, Jan 29 2016

PARI

x='x+O('x^30); Vec(serlaplace(exp(7*x - 225*x^2))) \\ G. C. Greubel, Oct 03 2018

Formula

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

a(n) = 15^n * Hermite(n, 7/30).

E.g.f.: exp(7*x - 225*x^2).

a(n) = numerator(Sum_{k=0..floor(n/2)} (-1)^k*n!*(7/15)^(n-2*k)/(k!*(n-2*k)!)). (End)