A160253 Numerator of Hermite(n, 10/29).

1, 20, -1282, -92920, 4610572, 717377200, -24427366520, -7728318032800, 133041452750480, 106653076504366400, 119080018350561760, -1791523146436431612800, -38033681428250725939520, 35399429559107921153964800, 1539633069292288796472840320

Offset

0,2

Links

G. C. Greubel, Table of n, a(n) for n = 0..371

Formula

From G. C. Greubel, Sep 26 2018: (Start)

a(n) = 29^n * Hermite(n, 10/29).

E.g.f.: exp(20*x - 841*x^2).

a(n) = numerator(Sum_{k=0..floor(n/2)} (-1)^k*n!*(20/29)^(n-2*k)/(k!*(n-2*k)!)). (End)

Example

Numerators of 1, 20/29, -1282/841, -92920/24389, 4610572/707281,...

Mathematica

Table[29^n*HermiteH[n, 10/29], {n, 0, 30}] (* G. C. Greubel, Sep 26 2018 *)

Prog

(PARI) a(n)=numerator(polhermite(n, 10/29)) \\ Charles R Greathouse IV, Jan 29 2016
(PARI) x='x+O('x^30); Vec(serlaplace(exp(20*x - 841*x^2))) \\ G. C. Greubel, Sep 26 2018
(Magma) [Numerator((&+[(-1)^k*Factorial(n)*(20/29)^(n-2*k)/( Factorial(k) *Factorial(n-2*k)): k in [0..Floor(n/2)]])): n in [0..30]]; // G. C. Greubel, Sep 26 2018

Crossrefs

Cf. A009973 (denominators).

Sequence in context: A093598 A174581 A153469 * A338961 A274645 A005982

Adjacent sequences: A160250 A160251 A160252 * A160254 A160255 A160256

Keyword

sign,frac

Author

N. J. A. Sloane, Nov 12 2009

Status

approved