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A160236 Numerator of Hermite(n, 5/29). 1
1, 10, -1582, -49460, 7488172, 407648600, -58899040520, -4702980076400, 646447502318480, 69747774931223200, -9088444540784918240, -1264042019751023406400, 155513980696092323212480, 27068563933615579666902400, -3129783062564598942695063680 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,2

LINKS

G. C. Greubel, Table of n, a(n) for n = 0..372

FORMULA

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

a(n) = 29^n * Hermite(n, 5/29).

E.g.f.: exp(10*x - 841*x^2).

a(n) = numerator(Sum_{k=0..floor(n/2)} (-1)^k*n!*(10/29)^(n-2*k)/(k!*(n-2*k)!)). (End)

EXAMPLE

Numerators of 1, 10/29, -1582/841, -49460/24389, 7488172/707281

MATHEMATICA

Numerator[HermiteH[Range[0, 20], 5/29]] (* Harvey P. Dale, Mar 10 2013 *)

Table[29^n*HermiteH[n, 5/29], {n, 0, 30}] (* G. C. Greubel, Sep 26 2018 *)

PROG

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

(PARI) x='x+O('x^30); Vec(serlaplace(exp(10*x - 841*x^2))) \\ G. C. Greubel, Sep 26 2018

(MAGMA) [Numerator((&+[(-1)^k*Factorial(n)*(10/29)^(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: A099128 A172958 A286397 * A204466 A117523 A203696

Adjacent sequences:  A160233 A160234 A160235 * A160237 A160238 A160239

KEYWORD

sign,frac

AUTHOR

N. J. A. Sloane, Nov 12 2009

STATUS

approved

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Last modified October 16 19:00 EDT 2018. Contains 316271 sequences. (Running on oeis4.)