OFFSET
1,2
COMMENTS
Conjecture: a(n) is divisible by (2*n-1)^2.
Robert G. Wilson v verified this conjecture up to 5000.
Note that sometimes a(n) is divisible by (2n-1)^3, for example, for n = 1,3,7,9,... when 2*n-1 = 1,5,13,17,... .
REFERENCES
M. Abramowitz and I. A. Stegun, Handbook of Mathematical Functions, 1972, Ch. 23.
LINKS
Robert G. Wilson v, Table of n, a(n) for n = 1..215
Vladimir Shevelev, On a Luschny question, arXiv:1708.08096 [math.NT], 2017.
FORMULA
MAPLE
A291897 := n -> euler(2*n-1, n)*2^(padic[ordp](2*n, 2)):
seq(A291897(n), n=1..15); # Peter Luschny, Sep 22 2017
MATHEMATICA
f[n_] := Numerator@ EulerE[2 n - 1, n]; Array[f, 15] (* Robert G. Wilson v, Sep 22 2017 *)
Table[2^IntegerExponent[2n, 2] EulerE[2 n-1, n], {n, 1, 15}] (* Peter Luschny, Sep 22 2017 *)
PROG
(PARI) a(n) = numerator(subst(eulerpol(2*n-1, 'x), 'x, n)); \\ Michel Marcus, Sep 21 2021
(Python)
from sympy import euler
def A291897(n): return euler((n<<1)-1, n).p # Chai Wah Wu, Jul 07 2022
CROSSREFS
KEYWORD
nonn,frac
AUTHOR
Vladimir Shevelev, Sep 22 2017
EXTENSIONS
More terms from Peter J. C. Moses, Sep 22 2017
STATUS
approved