A159943 Numerator of Hermite(n, 19/23).

1, 38, 386, -65740, -3723284, 136726888, 24891794104, 77945890928, -181386683278960, -7552427985415072, 1440171734736484384, 134631214005677868352, -11644732516647446263616, -2151777728648689174614400, 78394097345318787274427264, 34851107415866497970816728832

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, 19/23).

E.g.f.: exp(38*x - 529*x^2).

a(n) = numerator(Sum_{k=0..floor(n/2)} (-1)^k*n!*(38/23)^(n-2*k)/(k!*(n-2*k)!)). (End)

Example

Numerators of 1, 38/23, 386/529, -65740/12167, -3723284/279841, ...

Mathematica

Numerator[HermiteH[Range[0, 20], 19/23]] (* Harvey P. Dale, Jan 18 2012 *)
Table[23^n*HermiteH[n, 19/23], {n, 0, 30}] (* G. C. Greubel, Jul 16 2018 *)

Prog

(PARI) a(n)=numerator(polhermite(n, 19/23)) \\ Charles R Greathouse IV, Jan 29 2016
(PARI) x='x+O('x^30); Vec(serlaplace(exp(38*x - 529*x^2))) \\ G. C. Greubel, Jul 16 2018
(Magma) [Numerator((&+[(-1)^k*Factorial(n)*(38/23)^(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: A220918 A187078 A155193 * A221634 A251056 A267474

Adjacent sequences: A159940 A159941 A159942 * A159944 A159945 A159946

Keyword

sign,frac

Author

N. J. A. Sloane, Nov 12 2009

Status

approved