A159954 Numerator of Hermite(n, 5/24).

1, 5, -263, -4195, 206257, 5863925, -267690455, -11471314675, 482307383905, 28841445930725, -1105933509428135, -88593031827628675, 3060632198730188305, 321480678989935642325, -9851603557096146802295, -1345468115472901243865875, 35831586789290847966585025

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, 5/24).

E.g.f.: exp(5*x - 144*x^2).

a(n) = numerator(Sum_{k=0..floor(n/2)} (-1)^k*n!*(5/12)^(n-2*k)/(k!*(n-2*k)!)). (End)

Example

Numerators of 1, 5/12, -263/144, -4195/1728, 206257/20736, ...

Mathematica

Numerator[HermiteH[Range[0, 20], 5/24]] (* Harvey P. Dale, Feb 22 2016 *)
Table[12^n*HermiteH[n, 5/12], {n, 0, 30}] (* G. C. Greubel, Jul 16 2018 *)

Prog

(PARI) a(n)=numerator(polhermite(n, 5/24)) \\ Charles R Greathouse IV, Jan 29 2016
(PARI) x='x+O('x^30); Vec(serlaplace(exp(5*x - 144*x^2))) \\ G. C. Greubel, Jul 16 2018
(Magma) [Numerator((&+[(-1)^k*Factorial(n)*(5/12)^(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: A195575 A195553 A142254 * A079681 A086656 A034602

Adjacent sequences: A159951 A159952 A159953 * A159955 A159956 A159957

Keyword

sign,frac

Author

N. J. A. Sloane, Nov 12 2009

Status

approved