%I #20 Aug 10 2024 13:32:13

%S 1,2,7,68,1453,51974,2754739,202115720,19593627865,2424473303306,

%T 372795661540831,69721670054678732,15584255833611765637,

%U 4102656765126735657998,1256362298168756601126283,442800255547191861154809104,177962191835086481297819598769

%N Partial sums of A000364.

%C 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?

%F a(n) = Sum_{i=0..n} A000364(i).

%F 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

%F 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

%F 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

%t Accumulate[Table[Abs[EulerE[2n]],{n,0,20}]] (* _Harvey P. Dale_, Aug 10 2024 *)

%o (Python)

%o from sympy import euler

%o def A173226(n): return sum(abs(euler(i)) for i in range(0,(n<<1)+1,2)) # _Chai Wah Wu_, Apr 16 2023

%Y Cf. A000111, A000364, A000182, A011248, A060075, A013525, A000816, A002436, A028296, A122045.

%K easy,nonn

%O 0,2

%A _Jonathan Vos Post_, Feb 13 2010