A160061 Numerator of Hermite(n, 16/25).

1, 32, -226, -87232, -1943924, 373954432, 24116066824, -2032944101632, -276069795962224, 11495207545528832, 3473631846031942624, -32533875246088236032, -48803521890814034633024, -1073704571814725567776768, 758698684427656844617783424, 43068187908442716463862509568

Offset

0,2

Links

G. C. Greubel, Table of n, a(n) for n = 0..380

Formula

From G. C. Greubel, Sep 23 2018: (Start)

a(n) = 25^n * Hermite(n, 16/25).

E.g.f.: exp(32*x - 625*x^2).

a(n) = numerator(Sum_{k=0..floor(n/2)} (-1)^k*n!*(32/25)^(n-2*k)/(k!*(n-2*k)!)). (End)

Example

Numerators of 1, 32/25, -226/625, -87232/15625, -1943924/390625, ...

Mathematica

Numerator[Table[HermiteH[n, 16/25], {n, 0, 50}]] (* G. C. Greubel, Sep 23 2018 *)

Prog

(PARI) a(n)=numerator(polhermite(n, 16/25)) \\ Charles R Greathouse IV, Jan 29 2016
(PARI) x='x+O('x^30); Vec(serlaplace(exp(32*x - 625*x^2))) \\ G. C. Greubel, Sep 23 2018
(Magma) [Numerator((&+[(-1)^k*Factorial(n)*(32/25)^(n-2*k)/( Factorial(k) *Factorial(n-2*k)): k in [0..Floor(n/2)]])): n in [0..30]]; // G. C. Greubel, Sep 23 2018

Crossrefs

Cf. A009969 (denominators).

Sequence in context: A250232 A070053 A022146 * A269585 A199913 A301795

Adjacent sequences: A160058 A160059 A160060 * A160062 A160063 A160064

Keyword

sign,frac

Author

N. J. A. Sloane, Nov 12 2009

Status

approved