A160302 Numerator of Hermite(n, 4/31).

1, 8, -1858, -45616, 10348300, 433482208, -95979305336, -5766751265344, 1245171563867792, 98630939966871680, -20749930192050092576, -2061686107699674430208, 422201535258725661800128, 50928340670055096352718336, -10141700834614078614916251520

Offset

0,2

Links

Robert Israel, Table of n, a(n) for n = 0..368

Formula

From Robert Israel, Mar 27 2018: (Start)

a(n+2) = 8*a(n+1) - 1922*(n+1)*a(n).

E.g.f.: exp(-961*x^2+8*x). (End)

a(n) = 31^n * Hermite(n, 4/31). - G. C. Greubel, Jul 12 2018

Example

Numerators of 1, 8/31, -1858/961, -45616/29791, 10348300/923521, ...

Maple

seq(orthopoly[H](n, 4/31)*31^n, n=0..40); # Robert Israel, Mar 27 2018

Mathematica

Numerator[Table[HermiteH[n, 4/31], {n, 0, 40}]] (* Vincenzo Librandi, Mar 28 2018 *)

Prog

(PARI) a(n)=numerator(polhermite(n, 4/31)) \\ Charles R Greathouse IV, Jan 29 2016
(Magma) I:=[1, 8]; [n le 2 select I[n] else 8*Self(n-1)-1922*(n-2)*Self(n-2): n in [1..15]]; // Vincenzo Librandi, Mar 28 2018
(GAP) List(List([0..15], n->Sum([0..Int(n/2)], k->(-1)^k*Factorial(n)*(8/31)^(n-2*k)/(Factorial(k)*Factorial(n-2*k)))), NumeratorRat); # Muniru A Asiru, Jul 12 2018

Crossrefs

Cf. A009975 (denominators).

Sequence in context: A292695 A070903 A159386 * A002672 A027515 A297822

Adjacent sequences: A160299 A160300 A160301 * A160303 A160304 A160305

Keyword

sign,frac

Author

N. J. A. Sloane, Nov 12 2009

Status

approved