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A159676 Numerator of Hermite(n, 17/20). 1
1, 17, 89, -5287, -143279, 1793857, 173774569, 801539273, -229658228959, -5186652729103, 325211715731449, 15901904625640633, -445133395973297039, -45731838833083568863, 379905569368151630729, 134507543411892570538793, 1146911529897718806972481 (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) -17*a(n-1) +200*(n-1)*a(n-2)=0. - R. J. Mathar, Feb 17 2014

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

a(n) = 10^n * Hermite(n, 17/20).

E.g.f.: exp(17*x - 100*x^2).

a(n) = numerator(Sum_{k=0..floor(n/2)} (-1)^k*n!*(17/10)^(n-2*k)/(k!*(n-2*k)!)). (End)

EXAMPLE

Numerator of 1, 17/10, 89/100, -5287/1000, -143279/10000, 1793857/100000,...

MAPLE

A159676 := proc(n)

        orthopoly[H](n, 17/20) ;

        numer(%) ;

end proc: # R. J. Mathar, Feb 17 2014

MATHEMATICA

Numerator/@Table[HermiteH[n, 17/20], {n, 0, 35}]  (* Harvey P. Dale, Mar 13 2011 *)

Table[10^n*HermiteH[n, 17/20], {n, 0, 50}] (* G. C. Greubel, Jul 11 2018 *)

PROG

(PARI) a(n)=numerator(polhermite(n, 17/20)) \\ Charles R Greathouse IV, Jan 29 2016

(MAGMA) [Numerator((&+[(-1)^k*Factorial(n)*(17/10)^(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. A011557 (denominators).

Sequence in context: A267820 A200670 A057638 * A061971 A061222 A228462

Adjacent sequences:  A159673 A159674 A159675 * A159677 A159678 A159679

KEYWORD

sign,frac

AUTHOR

N. J. A. Sloane, Nov 12 2009

STATUS

approved

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Last modified July 17 16:38 EDT 2019. Contains 325107 sequences. (Running on oeis4.)