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

Author

N. J. A. Sloane, Nov 12 2009

Keywords

• sign
• frac

Links

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

Crossrefs

Cf. A159280.

Programs

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

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 *)

PARI

a(n)=numerator(polhermite(n,5/11)) \\ Charles R Greathouse IV, Jan 29 2016

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]