A159882 Numerator of Hermite(n, 13/23).

1, 26, -382, -64948, -476180, 262479256, 9343452856, -1423288542832, -106203113965168, 9285433263435680, 1252687316025657376, -65670013710482402624, -16286195340379143010112, 410305415218426865451392, 234668271507253831462816640, 23931248973260886967214336

Offset

0,2

Links

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

Formula

From G. C. Greubel, Jul 16 2018: (Start)

a(n) = 23^n * Hermite(n, 13/23).

E.g.f.: exp(26*x - 529*x^2).

a(n) = numerator(Sum_{k=0..floor(n/2)} (-1)^k*n!*(26/23)^(n-2*k)/(k!*(n-2*k)!)). (End)

Example

Numerators of 1, 26/23, -382/529, -64948/12167, -476180/279841, ...

Mathematica

Numerator[Table[HermiteH[n, 13/23], {n, 0, 30}]] (* or *) Table[23^n* HermiteH[n, 13/23], {n, 0, 30}] (* G. C. Greubel, Jul 16 2018 *)

Prog

(PARI) a(n)=numerator(polhermite(n, 13/23)) \\ Charles R Greathouse IV, Jan 29 2016
(PARI) x='x+O('x^30); Vec(serlaplace(exp(26*x - 529*x^2))) \\ G. C. Greubel, Jul 16 2018
(Magma) [Numerator((&+[(-1)^k*Factorial(n)*(26/23)^(n-2*k)/( Factorial(k) *Factorial(n-2*k)): k in [0..Floor(n/2)]])): n in [0..30]]; // G. C. Greubel, Jul 16 2018

Crossrefs

Cf. A009967 (denominators).

Sequence in context: A022654 A183187 A004318 * A036402 A036401 A232334

Adjacent sequences: A159879 A159880 A159881 * A159883 A159884 A159885

Keyword

sign,frac

Author

N. J. A. Sloane, Nov 12 2009

Status

approved