A159859 Numerator of Hermite(n, 2/23).

1, 4, -1042, -12632, 3256780, 66485744, -16962423224, -489901195808, 123664101613712, 4641180127773760, -1158964855054670624, -53739545172065063296, 13273074802437996468928, 735369564714290029481728, -179616392573875043315708800, -11610759562843564089946190336

Offset

0,2

Links

G. C. Greubel, Table of n, a(n) for n = 0..385

Formula

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

a(n) = 23^n * Hermite(n, 2/23).

E.g.f.: exp(4*x-529*x^2).

a(n) = numerator(Sum_{k=0..floor(n/2)} (-1)^k*n!*(4/23)^(n-2*k)/(k!*(n-2*k)!)). (End)

Mathematica

Numerator[Table[HermiteH[n, 2/23], {n, 0, 30}]] (* Vladimir Joseph Stephan Orlovsky, Jun 22 2011 *)
Table[23^n*HermiteH[n, 2/23], {n, 0, 30}] (* G. C. Greubel, Jul 09 2018 *)

Prog

(PARI) a(n)=numerator(polhermite(n, 2/23)) \\ Charles R Greathouse IV, Jan 29 2016
(Magma) [Numerator((&+[(-1)^k*Factorial(n)*(4/23)^(n-2*k)/( Factorial(k) *Factorial(n-2*k)): k in [0..Floor(n/2)]])): n in [0..30]]; // G. C. Greubel, Jul 09 2018

Crossrefs

Cf. A159858.

Sequence in context: A139300 A004804 A221228 * A110499 A009013 A351618

Adjacent sequences: A159856 A159857 A159858 * A159860 A159861 A159862

Keyword

sign,frac

Author

N. J. A. Sloane, Nov 12 2009

Status

approved