A158958 Numerator of Hermite(n, 3/4).

1, 3, 1, -45, -159, 963, 9249, -18477, -573375, -537597, 39670209, 162018387, -3004923231, -24568534845, 238806411489, 3468095137107, -18252483967359, -498673629451773, 986316931205505, 74767953434671827, 74383686760778721, -11739721489265156157

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) - 3*a(n-1) + 8*(n-1)*a(n-2) = 0. [DLMF] - R. J. Mathar, Feb 16 2014

From G. C. Greubel, Jul 10 2018: (Start)

a(n) = 2^n * Hermite(n, 3/4).

E.g.f.: exp(3*x - 4*x^2).

a(n) = numerator(Sum_{k=0..floor(n/2)} (-1)^k*n!*(3/2)^(n-2*k)/(k!*(n-2*k)!)). (End)

Example

Numerator of 1, 3/2, 1/4, -45/8, -159/16, 963/32, 9249/64, -18477/128, -573375/256, ...

Maple

A158958 := proc(n)
        orthopoly[H](n, 3/4) ;
        numer(%) ;
end proc: # R. J. Mathar, Feb 16 2014

Mathematica

Numerator[Table[HermiteH[n, 3/4], {n, 0, 50}]] (* Vladimir Joseph Stephan Orlovsky, Mar 23 2011 *)
Table[2^n*HermiteH[n, 3/4], {n, 0, 50}] (* G. C. Greubel, Jul 10 2018 *)

Prog

(PARI) a(n)=numerator(polhermite(n, 3/4)) \\ Charles R Greathouse IV, Jan 29 2016
(Magma) [Numerator((&+[(-1)^k*Factorial(n)*(3/2)^(n-2*k)/( Factorial(k) *Factorial(n-2*k)): k in [0..Floor(n/2)]])): n in [0..30]]; // G. C. Greubel, Jul 10 2018

Crossrefs

Cf. A000079 (denominators).

Sequence in context: A104097 A344379 A155812 * A098341 A354391 A223173

Adjacent sequences: A158955 A158956 A158957 * A158959 A158960 A158961

Keyword

sign,frac

Author

N. J. A. Sloane, Nov 12 2009

Status

approved