A160334 Numerator of Hermite(n, 23/31).

1, 46, 194, -167900, -8842004, 884083016, 125639477176, -4415829390416, -1893481677885040, -19202364475675424, 31870137298174352416, 1835095760938501860416, -589384037754831073199936, -69436314367007836275831680, 11532279106459848726285343616

Offset: 0

Author

N. J. A. Sloane, Nov 12 2009

Keywords

• sign
• frac

Examples

			Numerators of 1, 46/31, 194/961, -167900/29791, -8842004/923521, ...
		

Links

• Vincenzo Librandi, Table of n, a(n) for n = 0..200

Crossrefs

Cf. A009975 (denominators).

Programs

Magma

[Numerator((&+[(-1)^k*Factorial(n)*(46/31)^(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],23/31]] (* Harvey P. Dale, Aug 10 2014 *)
Table[31^n*HermiteH[n, 23/31], {n,0,30}] (* G. C. Greubel, Jul 12 2018 *)

PARI

a(n)=numerator(polhermite(n,23/31)) \\ Charles R Greathouse IV, Jan 29 2016

Formula

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

a(n) = 31^n * Hermite(n, 23/31).

E.g.f.: exp(46*x - 961*x^2).

a(n) = numerator(Sum_{k=0..floor(n/2)} (-1)^k*n!*(46/31)^(n-2*k)/(k!*(n-2*k)!)). (End)