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A160104 Numerator of Hermite(n, 5/27). 2
1, 10, -1358, -42740, 5512492, 304384600, -37142220680, -3034178687600, 348731717384080, 38877977386007200, -4187277821653825760, -608713688504523233600, 61068424818638825202880, 11260738942261526747094400, -1044883534589865025424443520 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,2

LINKS

G. C. Greubel, Table of n, a(n) for n = 0..376

FORMULA

From G. C. Greubel, Jul 12 2018: (Start)

a(n) = 27^n * Hermite(n, 5/27).

E.g.f.: exp(10*x - 729*x^2).

a(n) = numerator(Sum_{k=0..floor(n/2)} (-1)^k*n!*(10/27)^(n-2*k)/(k!*(n-2*k)!)). (End)

EXAMPLE

Numerators of 1, 10/27, -1358/729, -42740/19683, 5512492/531441..

MATHEMATICA

Numerator[Table[HermiteH[n, 5/27], {n, 0, 30}]] (* or *) Table[27^n* HermiteH[n, 5/27], {n, 0, 30}] (* G. C. Greubel, Jul 12 2018 *)

PROG

(PARI) a(n)=numerator(polhermite(n, 5/27)) \\ Charles R Greathouse IV, Jan 29 2016

(MAGMA) [Numerator((&+[(-1)^k*Factorial(n)*(10/27)^(n-2*k)/( Factorial(k) *Factorial(n-2*k)): k in [0..Floor(n/2)]])): n in [0..30]]; // G. C. Greubel, Jul 12 2018

CROSSREFS

Cf. A009971 (denominators).

Sequence in context: A013364 A013368 A317012 * A211914 A194792 A133216

Adjacent sequences:  A160101 A160102 A160103 * A160105 A160106 A160107

KEYWORD

sign,frac

AUTHOR

N. J. A. Sloane, Nov 12 2009

STATUS

approved

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Last modified November 17 10:32 EST 2018. Contains 317275 sequences. (Running on oeis4.)