|
|
A160260
|
|
Numerator of Hermite(n, 12/29).
|
|
1
|
|
|
1, 24, -1106, -107280, 3006156, 793927584, -6227509944, -8161777416384, -122559955912560, 106883437972961664, 4420515123955413216, -1691687063730285271296, -122388860352949901833536, 31207679045861280271833600, 3425139117578273280016104576
(list;
graph;
refs;
listen;
history;
text;
internal format)
|
|
|
OFFSET
|
0,2
|
|
LINKS
|
|
|
FORMULA
|
a(n) = 29^n * Hermite(n, 12/29).
E.g.f.: exp(24*x - 841*x^2).
a(n) = numerator(Sum_{k=0..floor(n/2)} (-1)^k*n!*(24/29)^(n-2*k)/(k!*(n-2*k)!)). (End)
|
|
EXAMPLE
|
Numerators of 1, 24/29, -1106/841, -107280/24389, 3006156/707281,...
|
|
MATHEMATICA
|
Table[29^n*HermiteH[n, 12/29], {n, 0, 30}] (* G. C. Greubel, Sep 26 2018 *)
HermiteH[Range[0, 20], 12/29]//Numerator (* Harvey P. Dale, Dec 27 2019 *)
|
|
PROG
|
(PARI) x='x+O('x^30); Vec(serlaplace(exp(24*x - 841*x^2))) \\ G. C. Greubel, Sep 26 2018
(Magma) [Numerator((&+[(-1)^k*Factorial(n)*(24/29)^(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
|
|
|
|