A160141 Numerator of Hermite(n, 14/27).

1, 28, -674, -100520, 133516, 589971088, 15545858824, -4725783030752, -290982960018800, 46974010390164928, 5133550692291311584, -541141652104447925888, -97483852261892597109056, 6738266481886428192282880, 2036380397264732274988968064, -80522844304853268561187040768

Offset

0,2

Links

G. C. Greubel, Table of n, a(n) for n = 0..376

Formula

From G. C. Greubel, Sep 24 2018: (Start)

a(n) = 27^n * Hermite(n, 14/27).

E.g.f.: exp(28*x - 729*x^2).

a(n) = numerator(Sum_{k=0..floor(n/2)} (-1)^k*n!*(28/27)^(n-2*k)/(k!*(n-2*k)!)). (End)

Example

Numerators of 1, 28/27, -674/729, -100520/19683, 133516/531441, ...

Mathematica

Table[27^n*HermiteH[n, 14/27], {n, 0, 30}] (* G. C. Greubel, Sep 24 2018 *)

Prog

(PARI) a(n)=numerator(polhermite(n, 14/27)) \\ Charles R Greathouse IV, Jan 29 2016
(PARI) x='x+O('x^30); Vec(serlaplace(exp(28*x - 729*x^2))) \\ G. C. Greubel, Sep 24 2018
(Magma) [Numerator((&+[(-1)^k*Factorial(n)*(28/27)^(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. A009971 (denominators).

Sequence in context: A236753 A269473 A278805 * A331476 A239408 A215857

Adjacent sequences: A160138 A160139 A160140 * A160142 A160143 A160144

Keyword

sign,frac

Author

N. J. A. Sloane, Nov 12 2009

Status

approved