A159877 Numerator of Hermite(n, 12/23).

1, 24, -482, -62352, 33420, 264675744, 6175426056, -1531951397568, -82502038912368, 10986387695118720, 1049257719206417376, -91053796553402040576, -14396552453405934395712, 810501742160249881655808, 217462224255991218838362240, -6786058422733831994965134336

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, 12/23).

E.g.f.: exp(24*x - 529*x^2).

a(n) = numerator(Sum_{k=0..floor(n/2)} (-1)^k*n!*(24/23)^(n-2*k)/(k!*(n-2*k)!)). (End)

Example

Numerators of 1, 24/23, -482/529, -62352/12167, 33420/279841, ...

Mathematica

HermiteH[Range[0, 20], 12/23]//Numerator (* Harvey P. Dale, Jan 09 2017 *)
Table[23^n*HermiteH[n, 12/23], {n, 0, 30}] (* G. C. Greubel, Jul 16 2018 *)

Prog

(PARI) a(n)=numerator(polhermite(n, 12/23)) \\ Charles R Greathouse IV, Jan 29 2016
(PARI) x='x+O('x^30); Vec(serlaplace(exp(24*x - 529*x^2))) \\ G. C. Greubel, Jul 16 2018
(Magma) [Numerator((&+[(-1)^k*Factorial(n)*(24/23)^(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: A052725 A360517 A006548 * A319426 A275041 A109143

Adjacent sequences: A159874 A159875 A159876 * A159878 A159879 A159880

Keyword

sign,frac

Author

N. J. A. Sloane, Nov 12 2009

Status

approved