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A158987 Numerator of Hermite(n, 3/7). 2
1, 6, -62, -1548, 8940, 660456, -417864, -390855312, -2058477168, 294079701600, 3580055071776, -266717777137344, -5459606030198592, 280902469732324992, 8640952900866956160, -333552471067548152064, -14703515590679714467584, 434789181089837215630848 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,2

LINKS

Vincenzo Librandi, Table of n, a(n) for n = 0..200

FORMULA

Conjecture: a(n) - 6*a(n-1) + 98*(n-1)*a(n-2) = 0. - R. J. Mathar, Feb 16 2014

From G. C. Greubel, Jul 09 2018: (Start)

a(n) = 7^n * Hermite(n, 3/7).

E.g.f.: exp(6*x-49*x^2).

a(n) = numerator(Sum_{k=0..floor(n/2)} (-1)^k*n!*(6/7)^(n-2*k)/(k!*(n-2*k)!)). (End)

EXAMPLE

Numerator of 1, 6/7, -62/49, -1548/343, 8940/2401, 660456/16807, -417864/117649, ...

MAPLE

A158987 := proc(n)

        orthopoly[H](n, 3/7) ;

        numer(%) ;

end proc: # R. J. Mathar, Feb 16 2014

MATHEMATICA

Numerator[Table[HermiteH[n, 3/7], {n, 0, 50}]] (* Vladimir Joseph Stephan Orlovsky, Mar 23 2011 *)

Table[7^n*HermiteH[n, 3/7], {n, 0, 30}] (* G. C. Greubel, Jul 09 2018 *)

PROG

(PARI) a(n)=numerator(polhermite(n, 3/7)) \\ Charles R Greathouse IV, Jan 29 2016

(MAGMA) [Numerator((&+[(-1)^k*Factorial(n)*(6/7)^(n-2*k)/( Factorial(k) *Factorial(n-2*k)): k in [0..Floor(n/2)]])): n in [0..30]]; // G. C. Greubel, Jul 09 2018

CROSSREFS

Cf. A000420 (denominators).

Sequence in context: A190726 A121251 A222079 * A055005 A027811 A027950

Adjacent sequences:  A158984 A158985 A158986 * A158988 A158989 A158990

KEYWORD

sign,frac

AUTHOR

N. J. A. Sloane, Nov 12 2009

STATUS

approved

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Last modified October 21 08:47 EDT 2019. Contains 328292 sequences. (Running on oeis4.)