A159618 Numerator of Hermite(n, 2/19).

1, 4, -706, -8600, 1494796, 30815984, -5272949624, -154586641184, 26031140834960, 997017002818624, -165162285134295584, -7859111900887647616, 1280282420933024937664, 73212475193022678695680, -11723880902105281350131584, -786927222859494361656459776

Offset

0,2

Links

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

Formula

From G. C. Greubel, Jun 09 2018: (Start)

a(n) = 19^n * Hermite(n,2/19).

E.g.f.: exp(4*x-361*x^2).

a(n) = Sum_{k=0..floor(n/2)} (-1)^k*n!*(4/19)^(n-2k)/(k!*(n-2k)!). (End)

Mathematica

Numerator[Table[HermiteH[n, 2/19], {n, 0, 30}]] (* Vladimir Joseph Stephan Orlovsky, May 20 2011 *)

Prog

(PARI) a(n)=numerator(polhermite(n, 2/19)) \\ Charles R Greathouse IV, Jan 29 2016
(Magma) [Numerator((&+[(-1)^k*Factorial(n)*(4/19)^(n-2*k)/( Factorial(k) *Factorial(n-2*k)): k in [0..Floor(n/2)]])): n in [0..30]]; // G. C. Greubel, Jun 09 2018

Crossrefs

Cf. A159564.

Sequence in context: A202368 A114765 A307920 * A219012 A370449 A364632

Adjacent sequences: A159615 A159616 A159617 * A159619 A159620 A159621

Keyword

sign,frac

Author

N. J. A. Sloane, Nov 12 2009

Status

approved