A159564 Numerator of Hermite(n, 1/19).

1, 2, -718, -4324, 1546540, 15580792, -5551847816, -78599686576, 27901839488912, 509795468640800, -180286562061668576, -4041296407709913152, 1423753283078352004288, 37861298642555391557504, -13287625717688301129132160, -409277258114326500121514752

Offset

0,2

Links

G. C. Greubel, Table of n, a(n) for n = 0..397

Formula

From G. C. Greubel, Jun 02 2018: (Start)

a(n) = 19^n * Hermite(n,1/19).

E.g.f.: exp(2*x-281*x^2).

a(n) = Sum_{k=0..floor(n/2)} (-1)^k*n!*(2/19)^(n-2k)/(k!*(n-2k)!). (End)

Mathematica

Numerator[Table[HermiteH[n, 1/19], {n, 0, 30}]] (* Vladimir Joseph Stephan Orlovsky, May 20 2011 *)

Prog

(PARI) a(n)=numerator(polhermite(n, 1/19)) \\ Charles R Greathouse IV, Jan 29 2016
(Magma) [Numerator((&+[(-1)^k*Factorial(n)*(2/19)^(n-2*k)/( Factorial(k) *Factorial(n-2*k)): k in [0..Floor(n/2)]])): n in [0..30]]; // G. C. Greubel, Jun 02 2018

Crossrefs

Cf. A159545, A159563.

Sequence in context: A062665 A256669 A361451 * A185667 A119781 A362187

Adjacent sequences: A159561 A159562 A159563 * A159565 A159566 A159567

Keyword

sign,frac

Author

N. J. A. Sloane, Nov 12 2009

Status

approved