A159525 Numerator of Hermite(n, 9/16).

1, 9, -47, -2727, -6495, 1337769, 16196721, -881636103, -22446986943, 700772486985, 32165881341201, -607495851269991, -50757023589840927, 476300415242137833, 88746390990674543025, -54812825197840109511, -170886386128875683593599

Offset

0,2

Links

Vincenzo Librandi, Table of n, a(n) for n = 0..200

DLMF Digital library of mathematical functions, Table 18.9.1 for H_n(x)

Formula

D-finite with recurrence a(n) -9*a(n-1) +128*(n-1)*a(n-2)=0. [DLMF] - R. J. Mathar, Feb 16 2014

From G. C. Greubel, Jun 09 2018: (Start)

a(n) = 16^n * Hermite(n,9/16).

E.g.f.: exp(18*x-252*x^2).

a(n) = Sum_{k=0..floor(n/2)} (-1)^k*n!*(9/8)^(n-2k)/(k!*(n-2k)!). (End)

Example

Numerator of 1, 9/8, -47/64, -2727/512, -6495/4096, 1337769/32768...

Maple

A159525 := proc(n)
        orthopoly[H](n, 9/16) ;
        numer(%) ;
end proc: # R. J. Mathar, Feb 16 2014

Mathematica

Numerator[Table[HermiteH[n, 9/16], {n, 0, 50}]] (* Vladimir Joseph Stephan Orlovsky, Apr 29 2011 *)

Prog

(PARI) a(n)=numerator(polhermite(n, 9/16)) \\ Charles R Greathouse IV, Jan 29 2016
(Magma) [Numerator((&+[(-1)^k*Factorial(n)*(9/8)^(n-2*k)/( Factorial(k) *Factorial(n-2*k)): k in [0..Floor(n/2)]])): n in [0..30]]; // G. C. Greubel, Jun 09 2018

Crossrefs

Cf. A001018 (denominators).

Sequence in context: A163614 A207318 A293042 * A173895 A341757 A286437

Adjacent sequences: A159522 A159523 A159524 * A159526 A159527 A159528

Keyword

sign,frac

Author

N. J. A. Sloane, Nov 12 2009

Status

approved