A159872 Numerator of Hermite(n, 8/23).

1, 16, -802, -46688, 1798540, 226360256, -5892512504, -1531215105152, 19140505922192, 13266452744761600, 30007346525073376, -139878952495176553984, -2587288738781628813632, 1734506561058255468362752, 63337674290134610196498560, -24678108393752726234245105664

Offset

0,2

Links

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

Formula

From G. C. Greubel, Jul 15 2018: (Start)

a(n) = 23^n * Hermite(n, 8/23).

E.g.f.: exp(16*x - 529*x^2).

a(n) = numerator(Sum_{k=0..floor(n/2)} (-1)^k*n!*(16/23)^(n-2*k)/(k!*(n-2*k)!)). (End)

Example

Numerators of 1, 16/23, -802/529, -46688/12167, 1798540/279841

Mathematica

Numerator[Table[HermiteH[n, 8/23], {n, 0, 30}]] (* or *) Table[23^n* HermiteH[n, 8/23], {n, 0, 30}] (* G. C. Greubel, Jul 15 2018 *)

Prog

(PARI) a(n)=numerator(polhermite(n, 8/23)) \\ Charles R Greathouse IV, Jan 29 2016
(PARI) x='x+O('x^30); Vec(serlaplace(exp(16*x - 529*x^2))) \\ G. C. Greubel, Jul 15 2018
(Magma) [Numerator((&+[(-1)^k*Factorial(n)*(16/23)^(n-2*k)/( Factorial(k) *Factorial(n-2*k)): k in [0..Floor(n/2)]])): n in [0..30]]; // G. C. Greubel, Jul 15 2018

Crossrefs

Cf. A009967 (denominators).

Sequence in context: A173984 A364510 A186855 * A220750 A166187 A363988

Adjacent sequences: A159869 A159870 A159871 * A159873 A159874 A159875

Keyword

sign,frac

Author

N. J. A. Sloane, Nov 12 2009

Status

approved