|
|
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
|
|
|
FORMULA
|
D-finite with recurrence a(n) - 6*a(n-1) + 98*(n-1)*a(n-2) = 0. [DLMF] - R. J. Mathar, Feb 16 2014
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
|
orthopoly[H](n, 3/7) ;
numer(%) ;
|
|
MATHEMATICA
|
Table[7^n*HermiteH[n, 3/7], {n, 0, 30}] (* G. C. Greubel, Jul 09 2018 *)
|
|
PROG
|
(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
|
|
|
KEYWORD
|
sign,frac
|
|
AUTHOR
|
|
|
STATUS
|
approved
|
|
|
|