OFFSET
0,2
COMMENTS
Partial sums of Euler numbers. Partial sums of secant or "Zig" numbers. The subsequence of prime partial sum of Euler numbers begins 2, 7, 1453, no more through a(17). What is the next such prime?
FORMULA
a(n) = Sum_{i=0..n} A000364(i).
G.f.: 1/U(0)/(1-x) where U(k)=1 + x - x*(2*k+1)*(2*k+2)/(1 - x*(2*k+1)*(2*k+2)/U(k+1)) ; (continued fraction, 2-step). - Sergei N. Gladkovskii, Oct 15 2012
G.f.: 1/(1-x)/Q(0), where Q(k)= 1 - x*(2*k+1)^2/(1 - x*(2*k+2)^2/Q(k+1)); (continued fraction). - Sergei N. Gladkovskii, Apr 27 2013
G.f.: Q(0)/(1-x), where Q(k) = 1 - x*(k+1)^2/( x*(k+1)^2 - 1/Q(k+1) ); (continued fraction). - Sergei N. Gladkovskii, Oct 22 2013
MATHEMATICA
Accumulate[Table[Abs[EulerE[2n]], {n, 0, 20}]] (* Harvey P. Dale, Aug 10 2024 *)
PROG
(Python)
from sympy import euler
def A173226(n): return sum(abs(euler(i)) for i in range(0, (n<<1)+1, 2)) # Chai Wah Wu, Apr 16 2023
CROSSREFS
KEYWORD
easy,nonn
AUTHOR
Jonathan Vos Post, Feb 13 2010
STATUS
approved