A159869 Numerator of Hermite(n, 5/23).

1, 10, -958, -30740, 2733292, 157424600, -12884868680, -1128180047600, 84143536968080, 10390351292567200, -697311246084385760, -116903029136204833600, 6946277990568033138880, 1553663637818936898774400, -80002471104083358804411520, -23812890514414926932690528000

Offset

0,2

Links

Robert Israel, Table of n, a(n) for n = 0..385

Formula

a(n) = 10*a(n-1) + 1058*(1-n)*a(n-2). - Robert Israel, Dec 07 2017

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

a(n) = 23^n * Hermite(n, 5/23).

E.g.f.: exp(10*x - 529*x^2).

a(n) = numerator(Sum_{k=0..floor(n/2)} (-1)^k*n!*(10/23)^(n-2*k)/(k!*(n-2*k)!)). (End)

Example

Numerators of 1, 10/23, -958/529, -30740/12167, 2733292/279841

Maple

f:= gfun:-rectoproc({a(n) = -(1058*n-1058)*a(n-2)+10*a(n-1), a(0) = 1, a(1) = 10}, a(n), remember):
map(f, [$0..40]); # Robert Israel, Dec 07 2017

Mathematica

Numerator[Table[HermiteH[n, 5/23], {n, 0, 30}]] (* Vladimir Joseph Stephan Orlovsky, Jun 22 2011 *)
Table[23^n*HermiteH[n, 5/23], {n, 0, 30}] (* G. C. Greubel, Jul 11 2018 *)

Prog

(PARI) a(n)=numerator(polhermite(n, 5/23)) \\ Charles R Greathouse IV, Jan 29 2016
(Magma) [Numerator((&+[(-1)^k*Factorial(n)*(10/23)^(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: A015008 A194791 A292669 * A006242 A163566 A168520

Adjacent sequences: A159866 A159867 A159868 * A159870 A159871 A159872

Keyword

sign,frac

Author

N. J. A. Sloane, Nov 12 2009

Status

approved