A160344 Numerator of Hermite(n, 26/31).

1, 52, 782, -159224, -12788660, 559103792, 151972419784, 1454980899424, -1968977929003888, -124758638617745600, 27571931007786483424, 3831601446637967570048, -383682490141447518907712, -108323545252613355018788096, 3953866345538313246451111040

Offset: 0

Author

N. J. A. Sloane, Nov 12 2009

Keywords

• sign
• frac

Examples

			Numerators of 1, 52/31, 782/961, -159224/29791, -12788660/923521, ...
		

Links

• Harvey P. Dale, Table of n, a(n) for n = 0..369

Crossrefs

Cf. A009975 (denominators).

Programs

Magma

[Numerator((&+[(-1)^k*Factorial(n)*(52/31)^(n-2*k)/( Factorial(k) *Factorial(n-2*k)): k in [0..Floor(n/2)]])): n in [0..30]]; // G. C. Greubel, Jul 12 2018

Mathematica

Numerator[HermiteH[Range[0,20],26/31]] (* Harvey P. Dale, Jan 26 2016 *)
Table[31^n*HermiteH[n, 26/31], {n,0,30}] (* G. C. Greubel, Jul 12 2018 *)

PARI

a(n)=numerator(polhermite(n,26/31)) \\ Charles R Greathouse IV, Jan 29 2016

Formula

From G. C. Greubel, Jul 12 2018: (Start)

a(n) = 31^n * Hermite(n, 26/31).

E.g.f.: exp(52*x - 961*x^2).

a(n) = numerator(Sum_{k=0..floor(n/2)} (-1)^k*n!*(52/31)^(n-2*k)/(k!*(n-2*k)!)). (End)