A159921 Numerator of Hermite(n, 18/23).

1, 36, 238, -67608, -3189300, 171302256, 23038278216, -258048705312, -179911241858928, -4292680465160640, 1558578348234929376, 101525379857857028736, -14483821141875255043392, -1810383783782862018394368, 134036659769169225204616320, 31640724357081844323823566336

Offset

0,2

Links

G. C. Greubel, Table of n, a(n) for n = 0..385

Formula

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

a(n) = 23^n * Hermite(n, 18/23).

E.g.f.: exp(36*x - 529*x^2).

a(n) = numerator(Sum_{k=0..floor(n/2)} (-1)^k*n!*(36/23)^(n-2*k)/(k!*(n-2*k)!)). (End)

Example

Numerators of 1, 36/23, 238/529, -67608/12167, -3189300/279841, ...

Mathematica

Numerator[Table[HermiteH[n, 18/23], {n, 0, 30}]] (* or *) Table[23^n* HermiteH[n, 18/23], {n, 0, 30}] (* G. C. Greubel, Jul 16 2018 *)

Prog

(PARI) a(n)=numerator(polhermite(n, 18/23)) \\ Charles R Greathouse IV, Jan 29 2016
(PARI) x='x+O('x^30); Vec(serlaplace(exp(36*x - 529*x^2))) \\ G. C. Greubel, Jul 16 2018
(Magma) [Numerator((&+[(-1)^k*Factorial(n)*(36/23)^(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. A009967 (denominators).

Sequence in context: A264522 A297656 A268794 * A326347 A129149 A223558

Adjacent sequences: A159918 A159919 A159920 * A159922 A159923 A159924

Keyword

sign,frac

Author

N. J. A. Sloane, Nov 12 2009

Status

approved