A159997 Numerator of Hermite(n, 19/24).

1, 19, 73, -9557, -244655, 6361219, 473166361, -2002025573, -991941869663, -14234228603405, 2300662982701801, 84707175049140619, -5679064003265633807, -400650213031877021597, 13650061580620869563065, 1874772828976324672777339, -23347582277731987729671359

Offset

0,2

Links

G. C. Greubel, Table of n, a(n) for n = 0..428

Formula

From G. C. Greubel, Jul 16 2018: (Start)

a(n) = 12^n * Hermite(n, 19/24).

E.g.f.: exp(19*x - 144*x^2).

a(n) = numerator(Sum_{k=0..floor(n/2)} (-1)^k*n!*(19/12)^(n-2*k)/(k!*(n-2*k)!)). (End)

Example

Numerators of 1, 19/12, 73/144, -9557/1728, -244655/20736, ...

Mathematica

Numerator[HermiteH[Range[0, 20], 19/24]] (* Harvey P. Dale, Jun 12 2016 *)
Table[12^n*HermiteH[n, 19/12], {n, 0, 30}] (* G. C. Greubel, Jul 16 2018 *)

Prog

(PARI) a(n)=numerator(polhermite(n, 19/24)) \\ Charles R Greathouse IV, Jan 29 2016
(PARI) x='x+O('x^30); Vec(serlaplace(exp(19*x - 144*x^2))) \\ G. C. Greubel, Jul 16 2018
(Magma) [Numerator((&+[(-1)^k*Factorial(n)*(19/12)^(n-2*k)/( Factorial(k) *Factorial(n-2*k)): k in [0..Floor(n/2)]])): n in [0..30]]; // G. C. Greubel, Jul 16 2018

Crossrefs

Cf. A001021 (denominators).

Sequence in context: A118593 A047979 A290241 * A073566 A098467 A244631

Adjacent sequences: A159994 A159995 A159996 * A159998 A159999 A160000

Keyword

sign,frac

Author

N. J. A. Sloane, Nov 12 2009

Status

approved