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A160220 Numerator of Hermite(n, 19/28). 1
1, 19, -31, -15485, -257759, 19383059, 873485761, -28992725309, -2947706709055, 34914759096979, 11062889692388641, 73329048495226499, -46309928432170516511, -1224828484332785265005, 212723654088018032104961, 10763608149690668144341699, -1046306531193423334034678399 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,2

LINKS

G. C. Greubel, Table of n, a(n) for n = 0..417

FORMULA

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

a(n) = 14^n * Hermite(n, 19/28).

E.g.f.: exp(19*x - 196*x^2).

a(n) = numerator(Sum_{k=0..floor(n/2)} (-1)^k*n!*(17/14)^(n-2*k)/(k!*(n-2*k)!)). (End)

EXAMPLE

Numerators of 1, 19/14, -31/196, -15485/2744, -257759/38416

MATHEMATICA

Numerator[HermiteH[Range[0, 20], 19/28]] (* Harvey P. Dale, Jul 26 2015 *)

Table[14^n*HermiteH[n, 19/28], {n, 0, 30}] (* G. C. Greubel, Sep 26 2018 *)

PROG

(PARI) a(n)=numerator(polhermite(n, 19/28)) \\ Charles R Greathouse IV, Jan 29 2016

(PARI) x='x+O('x^30); Vec(serlaplace(exp(19*x - 196*x^2))) \\ G. C. Greubel, Sep 26 2018

(MAGMA) [Numerator((&+[(-1)^k*Factorial(n)*(19/14)^(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. A001023 (denominators).

Sequence in context: A147210 A146816 A146659 * A133151 A184750 A101063

Adjacent sequences:  A160217 A160218 A160219 * A160221 A160222 A160223

KEYWORD

sign,frac

AUTHOR

N. J. A. Sloane, Nov 12 2009

STATUS

approved

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Last modified August 12 04:46 EDT 2022. Contains 356067 sequences. (Running on oeis4.)