A159327 Numerator of Hermite(n, 5/11).

1, 10, -142, -6260, 40492, 6464600, 15650680, -9230092400, -118813175920, 16681327127200, 425588368425760, -36112927963566400, -1494045516385037120, 89931487642346454400, 5599582070970791323520, -248692059422561874272000, -22813403511849591247097600

Offset

0,2

Links

G. C. Greubel, Table of n, a(n) for n = 0..434

Formula

From G. C. Greubel, Jun 26 2018: (Start)

a(n) = 11^n * Hermite(n,5/11).

E.g.f.: exp(10*x - 121*x^2).

a(n) = numerator(Sum_{k=0..floor(n/2)} (-1)^k*n!*(10/11)^(n-2*k)/(k!*(n-2*k)!)). (End)

a(n) = 10*a(n-1) - 242*(n-1)*a(n-2) for n>1. - Vincenzo Librandi, Jun 27 2018 [corrected by Georg Fischer, Dec 23 2019]

Mathematica

Numerator[Table[HermiteH[n, 5/11], {n, 0, 50}]] (* Vladimir Joseph Stephan Orlovsky, Apr 12 2011 *)
Table[11^n*HermiteH[n, 5/11], {n, 0, 30}] (* G. C. Greubel, Jun 26 2018 *)
RecurrenceTable[{a[n] == 10*a[n-1] - 242*(n-1)*a[n-2], a[0]==1, a[1]==10}, a, {n, 0, 30}] (* Georg Fischer, Dec 23 2019 *)

Prog

(PARI) a(n)=numerator(polhermite(n, 5/11)) \\ Charles R Greathouse IV, Jan 29 2016
(Magma) [Numerator((&+[(-1)^k*Factorial(n)*(10/11)^(n-2*k)/( Factorial(k) *Factorial(n-2*k)): k in [0..Floor(n/2)]])): n in [0..30]]; // G. C. Greubel, Jun 26 2018
(Magma) I:=[1, 10]; [n le 2 select I[n] else 10*Self(n-1)-242*(n-2)*Self(n-2): n in [1..25]]; // Vincenzo Librandi, Jun 27 2018

Crossrefs

Cf. A159280.

Sequence in context: A245988 A184710 A263055 * A356468 A276915 A284219

Adjacent sequences: A159324 A159325 A159326 * A159328 A159329 A159330

Keyword

sign,frac

Author

N. J. A. Sloane, Nov 12 2009

Status

approved