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A160067 Numerator of Hermite(n, 23/25). 1
1, 46, 866, -75164, -6705044, 67387976, 45006371896, 1564883287216, -321821122878064, -30452604524550944, 2219667824248876576, 482762276472335122496, -8313367865694637285184, -7623849068906980152558464, -215604829352183231133449344 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,2

LINKS

G. C. Greubel, Table of n, a(n) for n = 0..380

FORMULA

From G. C. Greubel, Sep 23 2018: (Start)

a(n) = 25^n * Hermite(n, 23/25).

E.g.f.: exp(46*x - 625*x^2).

a(n) = numerator(Sum_{k=0..floor(n/2)} (-1)^k*n!*(46/25)^(n-2*k)/(k!*(n-2*k)!)). (End)

EXAMPLE

Numerators of 1, 46/25, 866/625, -75164/15625, -6705044/390625, ...

MATHEMATICA

Table[25^n*HermiteH[n, 23/25], {n, 0, 30}] (* G. C. Greubel, Sep 23 2018 *)

PROG

(PARI) a(n)=numerator(polhermite(n, 23/25)) \\ Charles R Greathouse IV, Jan 29 2016

(PARI) x='x+O('x^30); Vec(serlaplace(exp(46*x - 625*x^2))) \\ G. C. Greubel, Sep 23 2018

(MAGMA) [Numerator((&+[(-1)^k*Factorial(n)*(46/25)^(n-2*k)/( Factorial(k) *Factorial(n-2*k)): k in [0..Floor(n/2)]])): n in [0..30]]; // G. C. Greubel, Sep 23 2018

CROSSREFS

Cf. A009969 (denominators).

Sequence in context: A078156 A066405 A113922 * A156842 A078427 A002138

Adjacent sequences:  A160064 A160065 A160066 * A160068 A160069 A160070

KEYWORD

sign,frac

AUTHOR

N. J. A. Sloane, Nov 12 2009

STATUS

approved

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Last modified August 15 16:02 EDT 2020. Contains 336505 sequences. (Running on oeis4.)