A159998 Numerator of Hermite(n, 23/24).

1, 23, 241, -7705, -385439, 11063, 555286609, 12752475143, -826150875455, -48383172864937, 1028570093285809, 163000649996592167, 490504894392176929, -552048633817202459785, -14533568902399966997231, 1891588006795761076916807, 106291541814670362197124481

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, 23/24).

E.g.f.: exp(23*x - 144*x^2).

a(n) = numerator(Sum_{k=0..floor(n/2)} (-1)^k*n!*(23/12)^(n-2*k)/(k!*(n-2*k)!)). (End)

Example

Numerators of 1, 23/12, 241/144, -7705/1728, -385439/20736, ...

Mathematica

Numerator[Table[HermiteH[n, 23/24], {n, 0, 30}]] (* or *) Table[12^n* HermiteH[n, 1/12], {n, 0, 30}] (* G. C. Greubel, Jul 16 2018 *)

Prog

(PARI) a(n)=numerator(polhermite(n, 23/24)) \\ Charles R Greathouse IV, Jan 29 2016
(PARI) x='x+O('x^30); Vec(serlaplace(exp(23*x - 144*x^2))) \\ G. C. Greubel, Jul 16 2018
(Magma) [Numerator((&+[(-1)^k*Factorial(n)*(23/12)^(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: A243449 A362431 A087332 * A268747 A158970 A161472

Adjacent sequences: A159995 A159996 A159997 * A159999 A160000 A160001

Keyword

sign,frac

Author

N. J. A. Sloane, Nov 12 2009

Status

approved