|
|
A160237
|
|
Numerator of Hermite(n, 6/29).
|
|
1
|
|
|
1, 12, -1538, -58824, 7054860, 480426192, -53566258296, -5491256229216, 564794050426512, 80667872425448640, -7581837866251154976, -1447815668591059984512, 122905376178286149551808, 30697575968981388522011904, -2319078043886628283835690880
(list;
graph;
refs;
listen;
history;
text;
internal format)
|
|
|
OFFSET
|
0,2
|
|
LINKS
|
|
|
FORMULA
|
a(n) = 29^n * Hermite(n, 6/29).
E.g.f.: exp(12*x - 841*x^2).
a(n) = numerator(Sum_{k=0..floor(n/2)} (-1)^k*n!*(12/29)^(n-2*k)/(k!*(n-2*k)!)). (End)
|
|
EXAMPLE
|
Numerators of 1, 12/29, -1538/841, -58824/24389, 7054860/707281,...
|
|
MATHEMATICA
|
Table[29^n*HermiteH[n, 6/29], {n, 0, 30}] (* G. C. Greubel, Sep 26 2018 *)
|
|
PROG
|
(PARI) x='x+O('x^30); Vec(serlaplace(exp(12*x - 841*x^2))) \\ G. C. Greubel, Sep 26 2018
(Magma) [Numerator((&+[(-1)^k*Factorial(n)*(12/29)^(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
|
|
|
KEYWORD
|
sign,frac
|
|
AUTHOR
|
|
|
STATUS
|
approved
|
|
|
|