A160307 Numerator of Hermite(n, 9/31).

1, 18, -1598, -97956, 7450860, 887201208, -55633142856, -11232600902064, 546301487747472, 182545898249590560, -6164096966563140576, -3619485909755267093568, 65170591691483110373568, 84652893673042176232776576, -104600317888637823603991680

Offset

0,2

Links

G. C. Greubel, Table of n, a(n) for n = 0..368

Formula

From Vincenzo Librandi, Jan 19 2017: (Start)

E.g.f.: exp(18*x - 961*x^2).

a(n+2) = -1922*(n+1)*a(n)+18*a(n+1). (End)

From G. C. Greubel, Oct 04 2018: (Start)

a(n) = 31^n * Hermite(n, 9/31).

a(n) = numerator(Sum_{k=0..floor(n/2)} (-1)^k*n!*(18/31)^(n-2*k)/(k!*(n-2*k)!)). (End)

Example

Numerators of 1, 18/31, -1598/961, -97956/29791, 7450860/923521, ...

Mathematica

Numerator[HermiteH[Range[0, 20], 9/31]] (* Harvey P. Dale, Jan 18 2017 *)
Table[31^n*HermiteH[n, 9/31], {n, 0, 30}] (* G. C. Greubel, Oct 04 2018 *)

Prog

(PARI) a(n)=numerator(polhermite(n, 9/31)) \\ Charles R Greathouse IV, Jan 29 2016
(PARI) x='x+O('x^30); Vec(serlaplace(exp(18*x - 961*x^2))) \\ G. C. Greubel, Oct 04 2018
(Sage) [numerator(hermite(n, 9/31)) for n in range(20)] # Bruno Berselli, Jan 19 2017
(Maxima) makelist(num(hermite(n, 9/31)), n, 0, 20); /* Bruno Berselli, Jan 19 2017 */
(Magma) [Numerator((&+[(-1)^k*Factorial(n)*(18/31)^(n-2*k)/( Factorial(k) *Factorial(n-2*k)): k in [0..Floor(n/2)]])): n in [0..30]]; // G. C. Greubel, Oct 04 2018

Crossrefs

Cf. A009975 (denominators).

Sequence in context: A210823 A258336 A211310 * A003030 A276016 A086366

Adjacent sequences: A160304 A160305 A160306 * A160308 A160309 A160310

Keyword

sign,frac

Author

N. J. A. Sloane, Nov 12 2009

Status

approved