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A159650 Numerator of Hermite(n, 12/19). 1
1, 24, -146, -38160, -599604, 95815584, 4464144456, -307933642944, -29952193511280, 1059772077373824, 220063883293269216, -2370021199600548096, -1804627869905557267776, -22777205204394225722880, 16391584262028099097996416, 623630012494691211958785024 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,2

LINKS

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

FORMULA

Conjecture: a(n) - 24*a(n-1) + 722*(n-1)*a(n-2) = 0. - R. J. Mathar, Feb 16 2014

From G. C. Greubel, Jul 11 2018: (Start)

a(n) = 19^n * Hermite(n, 12/19).

E.g.f.: exp(24*x - 361*x^2).

a(n) = numerator(Sum_{k=0..floor(n/2)} (-1)^k*n!*(24/19)^(n-2*k)/(k!*(n-2*k)!)). (End)

EXAMPLE

Numerator of 1, 24/19, -146/361, -38160/6859, -599604/130321, 95815584/2476099, ...

MAPLE

A159650 := proc(n)

        orthopoly[H](n, 12/19) ;

        numer(%) ;

end proc: # R. J. Mathar, Feb 16 2014

MATHEMATICA

Numerator[Table[HermiteH[n, 12/19], {n, 0, 30}]] (* Vladimir Joseph Stephan Orlovsky, Jun 16 2011 *)

Table[19^n*HermiteH[n, 12/19], {n, 0, 50}] (* G. C. Greubel, Jul 11 2018 *)

PROG

(PARI) a(n)=numerator(polhermite(n, 12/19)) \\ Charles R Greathouse IV, Jan 29 2016

(MAGMA) [Numerator((&+[(-1)^k*Factorial(n)*(24/19)^(n-2*k)/( Factorial(k) *Factorial(n-2*k)): k in [0..Floor(n/2)]])): n in [0..30]]; // G. C. Greubel, Jul 11 2018

CROSSREFS

Cf. A001029 (denominators).

Sequence in context: A290313 A042118 A039494 * A305160 A279459 A092181

Adjacent sequences:  A159647 A159648 A159649 * A159651 A159652 A159653

KEYWORD

sign,frac

AUTHOR

N. J. A. Sloane, Nov 12 2009

STATUS

approved

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Last modified November 20 02:34 EST 2019. Contains 329323 sequences. (Running on oeis4.)