A159660 Numerator of Hermite(n, 9/20).

1, 9, -119, -4671, 29361, 4001049, 6648441, -4741422831, -51980622879, 7118450923689, 157631179495401, -12818221231919391, -462152585977156719, 26604357682812127929, 1441035942685916620761, -61522878027700708614351, -4876813730307056239812159

Offset

0,2

Links

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

DLMF Digital library of mathematical functions, Table 18.9.1 for H_n(x)

Formula

D-finite with recurrence a(n) -9*a(n-1) +200*(n-1)*a(n-2)=0. [DLMF] - 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