A160309 Numerator of Hermite(n, 11/31).

1, 22, -1438, -116204, 5735020, 1019546792, -32683512776, -12476450886416, 165242061387152, 195473234180049760, 1442053974086139424, -3725270373510661319872, -112443853337363708739392, 83445871121227891089261184, 4645331284154383230526194560

Offset

0,2

Links

G. C. Greubel, Table of n, a(n) for n = 0..368

Formula

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

a(n) = 31^n * Hermite(n, 11/31).

a(n+2) = 22*a(n+1) - 1922*(n+1)*a(n)

E.g.f.: exp(22*x - 961*x^2).

a(n) = numerator(Sum_{k=0..floor(n/2)} (-1)^k*n!*(22/31)^(n-2*k)/(k!*(n-2*k)!)). (End)

Example

Numerators of 1, 22/31, -1438/961, -116204/29791, 5735020/923521, ...

Mathematica

Table[31^n*HermiteH[n, 11/31], {n, 0, 30}] (* G. C. Greubel, Oct 04 2018 *)

Prog

(PARI) a(n)=numerator(polhermite(n, 11/31)) \\ Charles R Greathouse IV, Jan 29 2016
(PARI) x='x+O('x^30); Vec(serlaplace(exp(22*x - 961*x^2))) \\ G. C. Greubel, Oct 04 2018
(Magma) [Numerator((&+[(-1)^k*Factorial(n)*(22/31)^(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. A009975 (denominators).

Sequence in context: A160259 A055475 A348813 * A367369 A033526 A078399

Adjacent sequences: A160306 A160307 A160308 * A160310 A160311 A160312

Keyword

sign,frac

Author

N. J. A. Sloane, Nov 12 2009

Status

approved