A160298 Numerator of Hermite(n, 29/30).

1, 29, 391, -14761, -955919, -1151851, 2117414071, 64515005759, -4798919156639, -371422676274931, 8664364972414951, 1922668627437223079, 12868783582225461841, -10009215864276466233211, -365549644020036472532969, 52457120268360679565773199

Offset

0,2

Links

G. C. Greubel, Table of n, a(n) for n = 0..412

Formula

From G. C. Greubel, Oct 04 2018: (Start)

a(n) = 15^n * Hermite(n, 29/30).

E.g.f.: exp(29*x - 225*x^2).

a(n) = numerator(Sum_{k=0..floor(n/2)} (-1)^k*n!*(29/15)^(n-2*k)/(k!*(n-2*k)!)). (End)

Example

Numerators of 1, 29/15, 391/225, -14761/3375, -955919/50625, ...

Mathematica

Table[15^n*HermiteH[n, 29/30], {n, 0, 30}] (* G. C. Greubel, Oct 04 2018 *)

Prog

(PARI) a(n)=numerator(polhermite(n, 29/30)) \\ Charles R Greathouse IV, Jan 29 2016
(PARI) x='x+O('x^30); Vec(serlaplace(exp(29*x - 225*x^2))) \\ G. C. Greubel, Oct 04 2018
(Magma) [Numerator((&+[(-1)^k*Factorial(n)*(29/15)^(n-2*k)/( Factorial(k) *Factorial(n-2*k)): k in [0..Floor(n/2)]])): n in [0..30]]; // G. C. Greubel, Oct 04 2018

Crossrefs

Cf. A001024 (denominators).

Sequence in context: A125441 A142756 A142327 * A077508 A077514 A210260

Adjacent sequences: A160295 A160296 A160297 * A160299 A160300 A160301

Keyword

sign,frac

Author

N. J. A. Sloane, Nov 12 2009

Status

approved