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A160192 Numerator of Hermite(n, 3/28). 1
1, 3, -383, -3501, 439905, 6809283, -841785951, -18540791469, 2254238275137, 64906636872195, -7758232724066751, -277708714711204653, 32620373362042216353, 1404202914087633336771, -162020813910704234524575, -8192328034245044455772973, 928105401692205765637182081 (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 24 2018: (Start)

a(n) = 14^n * Hermite(n, 3/28).

E.g.f.: exp(3*x - 196*x^2).

a(n) = numerator(Sum_{k=0..floor(n/2)} (-1)^k*n!*(3/14)^(n-2*k)/(k!*(n-2*k)!)). (End)

EXAMPLE

Numerators of 1, 3/14, -383/196, -3501/2744, 439905/38416, ...

MATHEMATICA

Table[14^n*HermiteH[n, 3/28], {n, 0, 30}] (* G. C. Greubel, Sep 24 2018 *)

PROG

(PARI) a(n)=numerator(polhermite(n, 3/28)) \\ Charles R Greathouse IV, Jan 29 2016

(PARI) x='x+O('x^30); Vec(serlaplace(exp(3*x - 196*x^2))) \\ G. C. Greubel, Sep 24 2018

(MAGMA) [Numerator((&+[(-1)^k*Factorial(n)*(3/14)^(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. A001023 (denominators)

Sequence in context: A136025 A157577 A062604 * A304424 A316279 A305958

Adjacent sequences:  A160189 A160190 A160191 * A160193 A160194 A160195

KEYWORD

sign,frac

AUTHOR

N. J. A. Sloane, Nov 12 2009

STATUS

approved

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Last modified October 15 09:40 EDT 2018. Contains 316211 sequences. (Running on oeis4.)