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A159660 Numerator of Hermite(n, 9/20). 1
1, 9, -119, -4671, 29361, 4001049, 6648441, -4741422831, -51980622879, 7118450923689, 157631179495401, -12818221231919391, -462152585977156719, 26604357682812127929, 1441035942685916620761, -61522878027700708614351, -4876813730307056239812159 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,2

LINKS

G. C. Greubel, Table of n, a(n) for n = 0..441

FORMULA

Conjecture: a(n) -9*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, 9/20).

E.g.f.: exp(9*x - 100*x^2).

a(n) = numerator(Sum_{k=0..floor(n/2)} (-1)^k*n!*(9/10)^(n-2*k)/(k!*(n-2*k)!)). (End)

EXAMPLE

Numerator of 1, 9/10, -119/100, -4671/1000, 29361/10000, 4001049/100000,...

MAPLE

A159660 := proc(n)

        orthopoly[H](n, 9/20) ;

        numer(%) ;

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

MATHEMATICA

Numerator[Table[HermiteH[n, 9/20], {n, 0, 30}]] (* Vladimir Joseph Stephan Orlovsky, Jun 16 2011 *)

Table[10^n*HermiteH[n, 9/20], {n, 0, 50}] (* G. C. Greubel, Jul 11 2018 *)

PROG

(PARI) a(n)=numerator(polhermite(n, 9/20)) \\ Charles R Greathouse IV, Jan 29 2016

(MAGMA) [Numerator((&+[(-1)^k*Factorial(n)*(9/10)^(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: A210046 A130652 A054051 * A061172 A167593 A214698

Adjacent sequences:  A159657 A159658 A159659 * A159661 A159662 A159663

KEYWORD

sign,frac

AUTHOR

N. J. A. Sloane, Nov 12 2009

STATUS

approved

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Last modified October 14 01:36 EDT 2019. Contains 327994 sequences. (Running on oeis4.)