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A173226 Partial sums of A000364. 1
1, 2, 7, 68, 1453, 51974, 2754739, 202115720, 19593627865, 2424473303306, 372795661540831, 69721670054678732, 15584255833611765637, 4102656765126735657998, 1256362298168756601126283 (list; graph; refs; listen; history; text; internal format)
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?

LINKS

Table of n, a(n) for n=0..14.

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

CROSSREFS

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

Sequence in context: A225156 A260968 A322223 * A094223 A217069 A319640

Adjacent sequences:  A173223 A173224 A173225 * A173227 A173228 A173229

KEYWORD

easy,nonn

AUTHOR

Jonathan Vos Post, Feb 13 2010

STATUS

approved

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Last modified January 19 18:27 EST 2019. Contains 319309 sequences. (Running on oeis4.)