|
|
A160003
|
|
Numerator of Hermite(n, 1/25).
|
|
1
|
|
|
1, 2, -1246, -7492, 4657516, 46775032, -29015924936, -408844589872, 253071654010256, 4594589206740512, -2837866929201898976, -63108098942660197952, 38894454078640790524096, 1024410392297184550328192, -629986057993318476915903616, -19187153981187366584575167232
(list;
graph;
refs;
listen;
history;
text;
internal format)
|
|
|
OFFSET
|
0,2
|
|
LINKS
|
|
|
FORMULA
|
a(n) = 25^n * Hermite(n, 1/25).
E.g.f.: exp(2*x - 625*x^2).
a(n) = numerator(Sum_{k=0..floor(n/2)} (-1)^k*n!*(2/25)^(n-2*k)/(k!*(n-2*k)!)). (End)
|
|
EXAMPLE
|
Numerators of 1, 2/25, -1246/625, -7492/15625, 4657516/390625, ...
|
|
MATHEMATICA
|
Numerator[Table[HermiteH[n, 1/25], {n, 0, 30}]] (* or *) Table[25^n* HermiteH[n, 1/25], {n, 0, 30}] (* G. C. Greubel, Jul 16 2018 *)
|
|
PROG
|
(PARI) x='x+O('x^30); Vec(serlaplace(exp(2*x - 625*x^2))) \\ G. C. Greubel, Jul 16 2018
(Magma) [Numerator((&+[(-1)^k*Factorial(n)*(2/25)^(n-2*k)/( Factorial(k) *Factorial(n-2*k)): k in [0..Floor(n/2)]])): n in [0..30]]; // G. C. Greubel, Jul 16 2018
|
|
CROSSREFS
|
|
|
KEYWORD
|
sign,frac
|
|
AUTHOR
|
|
|
STATUS
|
approved
|
|
|
|