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A160252 Numerator of Hermite(n, 9/29). 1
1, 18, -1358, -84996, 5322540, 667658808, -32744702856, -7327417341744, 253642619275152, 103163294897460000, -1982702662432970976, -1770895268099070677568, 4807849834551556801728, 35830291388333570578463616, 539816800507699929385760640 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,2

LINKS

G. C. Greubel, Table of n, a(n) for n = 0..371

FORMULA

From G. C. Greubel, Sep 26 2018: (Start)

a(n) = 29^n * Hermite(n, 9/29).

E.g.f.: exp(18*x - 841*x^2).

a(n) = numerator(Sum_{k=0..floor(n/2)} (-1)^k*n!*(18/29)^(n-2*k)/(k!*(n-2*k)!)). (End)

EXAMPLE

Numerators of 1, 18/29, -1358/841, -84996/24389, 5322540/707281,...

MATHEMATICA

Table[29^n*HermiteH[n, 9/29], {n, 0, 30}] (* G. C. Greubel, Sep 26 2018 *)

PROG

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

(PARI) x='x+O('x^30); Vec(serlaplace(exp(18*x - 841*x^2))) \\ G. C. Greubel, Sep 26 2018

(MAGMA) [Numerator((&+[(-1)^k*Factorial(n)*(18/29)^(n-2*k)/( Factorial(k) *Factorial(n-2*k)): k in [0..Floor(n/2)]])): n in [0..30]]; // G. C. Greubel, Sep 26 2018

CROSSREFS

Cf. A009973 (denominators).

Sequence in context: A182286 A292609 A275047 * A276015 A210823 A258336

Adjacent sequences:  A160249 A160250 A160251 * A160253 A160254 A160255

KEYWORD

sign,frac

AUTHOR

N. J. A. Sloane, Nov 12 2009

STATUS

approved

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Last modified December 5 13:26 EST 2019. Contains 329751 sequences. (Running on oeis4.)