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A160150 Numerator of Hermite(n, 22/27). 1
1, 44, 478, -107272, -6810740, 325937744, 63991555336, -35674949728, -654667511547248, -28389257894451520, 7341419739167121376, 736937848624456502144, -85316424437286206533952, -16647387274774084049005312, 884602468694263060488292480 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,2

LINKS

G. C. Greubel, Table of n, a(n) for n = 0..375

FORMULA

From G. C. Greubel, Sep 24 2018: (Start)

a(n) = 27^n * Hermite(n, 22/27).

E.g.f.: exp(44*x - 729*x^2).

a(n) = numerator(Sum_{k=0..floor(n/2)} (-1)^k*n!*(44/27)^(n-2*k)/(k!*(n-2*k)!)). (End)

EXAMPLE

Numerators of 1, 44/27, 478/729, -107272/19683, -6810740/531441, ...

MATHEMATICA

Numerator[HermiteH[Range[0, 20], 22/27]] (* Harvey P. Dale, Jul 29 2013 *)

Table[27^n*HermiteH[n, 22/27], {n, 0, 30}] (* G. C. Greubel, Sep 24 2018 *)

PROG

(PARI) a(n)=numerator(polhermite(n, 22/27)) \\ Charles R Greathouse IV, Jan 29 2016

(PARI) x='x+O('x^30); Vec(serlaplace(exp(44*x - 729*x^2))) \\ G. C. Greubel, Sep 24 2018

(Magma) [Numerator((&+[(-1)^k*Factorial(n)*(44/27)^(n-2*k)/( Factorial(k) *Factorial(n-2*k)): k in [0..Floor(n/2)]])): n in [0..30]]; // G. C. Greubel, Sep 24 2018

CROSSREFS

Cf. A009971 (denominators)

Sequence in context: A231242 A221730 A306036 * A210119 A272186 A222514

Adjacent sequences: A160147 A160148 A160149 * A160151 A160152 A160153

KEYWORD

sign,frac

AUTHOR

N. J. A. Sloane, Nov 12 2009

STATUS

approved

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Last modified December 2 18:27 EST 2022. Contains 358510 sequences. (Running on oeis4.)