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A159658 Numerator of Hermite(n, 3/20). 1
1, 3, -191, -1773, 109281, 1746243, -104042271, -2407618413, 138436324161, 4267498433283, -236382888189951, -9244145531135853, 492309917424484641, 23662879026999501123, -1209017148222661563231, -69883112720266587834093, 3417402106507184926190721 (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) -3*a(n-1) +200*(n-1)*a(n-2)=0. - R. J. Mathar, Feb 16 2014

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

a(n) = 10^n * Hermite(n, 3/20).

E.g.f.: exp(3*x - 100*x^2).

a(n) = numerator(Sum_{k=0..floor(n/2)} (-1)^k*n!*(3/10)^(n-2*k)/(k!*(n-2*k)!)). (End)

EXAMPLE

Numerator of 1, 3/10, -191/100, -1773/1000, 109281/10000, 1746243/100000..

MAPLE

A159658 := proc(n)

        orthopoly[H](n, 3/20) ;

        numer(%) ;

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

MATHEMATICA

Numerator[Table[HermiteH[n, 3/20], {n, 0, 30}]] (* Vladimir Joseph Stephan Orlovsky, Jun 16 2011 *)

Table[10^n*HermiteH[n, 3/20], {n, 0, 50}] (* G. C. Greubel, Jul 11 2018 *)

PROG

(PARI) a(n)=numerator(polhermite(n, 3/20)) \\ Charles R Greathouse IV, Jan 29 2016

(MAGMA) [Numerator((&+[(-1)^k*Factorial(n)*(3/10)^(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: A158469 A261000 A032594 * A257038 A202109 A230171

Adjacent sequences:  A159655 A159656 A159657 * A159659 A159660 A159661

KEYWORD

sign,frac

AUTHOR

N. J. A. Sloane, Nov 12 2009

STATUS

approved

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Last modified October 21 03:24 EDT 2019. Contains 328291 sequences. (Running on oeis4.)