A159889 Numerator of Hermite(n, 16/23).

1, 32, -34, -68800, -2093684, 224163712, 18248827144, -839028775168, -161999734633840, 1917548044739072, 1603923010615074784, 31037878026343011328, -17673243900695263973696, -959600704244699318978560, 212370574074332282486900864, 21009464001651119352291258368

Offset

0,2

Links

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

Formula

From G. C. Greubel, Jul 11 2018: (Start)

a(n) = 23^n * Hermite(n, 16/23).

E.g.f.: exp(32*x - 529*x^2).

a(n) = numerator(Sum_{k=0..floor(n/2)} (-1)^k*n!*(32/23)^(n-2*k)/(k!*(n-2*k)!)). (End)

Example

Numerators of 1, 32/23, -34/529, -68800/12167, -2093684/279841..

Mathematica

Numerator[Table[HermiteH[n, 16/23], {n, 0, 40}]] (* Vladimir Joseph Stephan Orlovsky, Mar 21 2011*)
Table[23^n*HermiteH[n, 16/23], {n, 0, 30}] (* G. C. Greubel, Jul 11 2018 *)

Prog

(PARI) a(n)=numerator(polhermite(n, 16/23)) \\ Charles R Greathouse IV, Jan 29 2016
(Magma) [Numerator((&+[(-1)^k*Factorial(n)*(32/23)^(n-2*k)/( Factorial(k) *Factorial(n-2*k)): k in [0..Floor(n/2)]])): n in [0..30]]; // G. C. Greubel, Jul 11 2018

Crossrefs

Cf. A009967 (denominators)

Sequence in context: A029925 A074287 A223589 * A345490 A095481 A095475

Adjacent sequences: A159886 A159887 A159888 * A159890 A159891 A159892

Keyword

sign,frac

Author

N. J. A. Sloane, Nov 12 2009

Status

approved