A160315 Numerator of Hermite(n, 17/31).

1, 34, -766, -156740, -912404, 1173995384, 48684045496, -11883257221424, -1059025893631600, 146710082653141024, 23307172718246211616, -2027323916172999286336, -561689258759043381720896, 27660764004806580561543040, 14974833795516881674770770816

Offset: 0

Author

N. J. A. Sloane, Nov 12 2009

Keywords

• sign
• frac

Examples

			Numerators of 1, 34/31, -766/961, -156740/29791, -912404/923521, ...
		

Links

• G. C. Greubel, Table of n, a(n) for n = 0..368

Crossrefs

Cf. A009975 (denominators).

Programs

Magma

[Numerator((&+[(-1)^k*Factorial(n)*(34/31)^(n-2*k)/( Factorial(k) *Factorial(n-2*k)): k in [0..Floor(n/2)]])): n in [0..30]]; // G. C. Greubel, Oct 04 2018

Mathematica

Numerator[HermiteH[Range[0,20],17/31]] (* Harvey P. Dale, Feb 24 2013 *)
Table[31^n*HermiteH[n, 17/31], {n, 0, 30}] (* G. C. Greubel, Oct 04 2018 *)

PARI

a(n)=numerator(polhermite(n, 17/31)) \\ Charles R Greathouse IV, Jan 29 2016

PARI

x='x+O('x^30); Vec(serlaplace(exp(34*x - 961*x^2))) \\ G. C. Greubel, Oct 04 2018

Formula

From G. C. Greubel, Oct 04 2018: (Start)

a(n) = 31^n * Hermite(n, 17/31).

a(n+2) = 34*a(n+1) - 1922*(n+1)*a(n)

E.g.f.: exp(34*x - 961*x^2).

a(n) = numerator(Sum_{k=0..floor(n/2)} (-1)^k*n!*(34/31)^(n-2*k)/(k!*(n-2*k)!)). (End)