A158981 Numerator of Hermite(n, 2/7).

1, 4, -82, -1112, 19660, 514544, -7575224, -332852768, 3865192592, 276417340480, -2303430504224, -280102715687296, 1362687220804288, 334851542531477248, -396657349178753920, -461002945749901799936, -1260925479706838937344, 717808917017018666550272

Offset

0,2

Links

G. C. Greubel, Table of n, a(n) for n = 0..450

Formula

From G. C. Greubel, Jul 10 2018: (Start)

a(n) = 7^n * Hermite(n, 2/7).

E.g.f.: exp(4*x - 49*x^2).

a(n) = numerator(Sum_{k=0..floor(n/2)} (-1)^k*n!*(4/7)^(n-2*k)/(k!*(n-2*k)!)). (End)

Mathematica

Numerator[Table[HermiteH[n, 2/7], {n, 0, 50}]] (* Vladimir Joseph Stephan Orlovsky, Apr 01 2011*)
Table[7^n*HermiteH[n, 2/7], {n, 0, 50}] (* G. C. Greubel, Jul 10 2018 *)

Prog

(PARI) a(n)=numerator(polhermite(n, 2/7)) \\ Charles R Greathouse IV, Jan 29 2016
(Magma) [Numerator((&+[(-1)^k*Factorial(n)*(4/7)^(n-2*k)/( Factorial(k) *Factorial(n-2*k)): k in [0..Floor(n/2)]])): n in [0..30]]; // G. C. Greubel, Jul 10 2018

Crossrefs

Cf. A158980.

Sequence in context: A357781 A318868 A289224 * A317889 A291371 A007154

Adjacent sequences: A158978 A158979 A158980 * A158982 A158983 A158984

Keyword

sign,frac

Author

N. J. A. Sloane, Nov 12 2009

Status

approved