A160140 Numerator of Hermite(n, 13/27).

1, 26, -782, -96148, 920620, 584671256, 8490132856, -4893960693232, -213893273952368, 51521932403096480, 4146277783283481376, -643386552071776162624, -83226053442166654536512, 9092813725551462723320192, 1813879773807164800891373440

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, 13/27).

E.g.f.: exp(26*x - 729*x^2).

a(n) = numerator(Sum_{k=0..floor(n/2)} (-1)^k*n!*(26/27)^(n-2*k)/(k!*(n-2*k)!)). (End)

Example

Numerators of 1, 26/27, -782/729, -96148/19683, 920620/531441

Mathematica

Table[27^n*HermiteH[n, 13/27], {n, 0, 30}] (* G. C. Greubel, Sep 24 2018 *)

Prog

(PARI) a(n)=numerator(polhermite(n, 13/27)) \\ Charles R Greathouse IV, Jan 29 2016
(PARI) x='x+O('x^30); Vec(serlaplace(exp(26*x - 729*x^2))) \\ G. C. Greubel, Sep 24 2018
(Magma) [Numerator((&+[(-1)^k*Factorial(n)*(26/27)^(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: A282790 A180792 A091742 * A139670 A231282 A357140

Adjacent sequences: A160137 A160138 A160139 * A160141 A160142 A160143

Keyword

sign,frac

Author

N. J. A. Sloane, Nov 12 2009

Status

approved