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A141458 a(n) = A000111(2n) + A000111(2n+1).

%I A141458 #22 Apr 17 2023 11:05:54
%S A141458 2,3,21,333,9321,404313,25071021,2103118293,229256855121,
%T A141458 31493764788273,5321869241361621,1084772760899990253,
%U A141458 262436014353765070521,74338674113237083780233,24371443829213227706941821,9155506650374192400724494213,3906927095300068860534174415521
%N A141458 a(n) = A000111(2n) + A000111(2n+1).
%H A141458 Alois P. Heinz, <a href="/A141458/b141458.txt">Table of n, a(n) for n = 0..100</a>
%F A141458 a(2n) == 21 (mod 100), n>0.
%F A141458 a(n) = (2n)! * [x^(2n)] sec(x) + sec(x)^2. - _Ira M. Gessel_, Apr 18 2013
%p A141458 A000111 := proc(n) if n = 0 then 1; else 2^n*abs(euler(n, 1/2)+euler(n, 1) ); end if; end proc:
%p A141458 A141458 := proc(n) A000111(2*n)+A000111(2*n+1) ; end proc: # _R. J. Mathar_, Jul 07 2011
%t A141458 terms = 20;
%t A141458 CoefficientList[Sec[x] + Sec[x]^2 + O[x]^(2 terms - 1), x^2] Range[0, 2 terms - 2, 2]!  (* _Jean-François Alcover_, Nov 19 2020 *)
%o A141458 (Python)
%o A141458 from itertools import accumulate, islice
%o A141458 def A141458_gen(): # generator of terms
%o A141458     yield 2
%o A141458     blist = (0,1)
%o A141458     while True:
%o A141458         yield (blist := tuple(accumulate(reversed(blist),initial=0)))[-1] + (blist := tuple(accumulate(reversed(blist),initial=0)))[-1]
%o A141458 A141458_list = list(islice(A141458_gen(),30)) # _Chai Wah Wu_, Apr 17 2023
%Y A141458 Cf. A000111.
%K A141458 nonn
%O A141458 0,1
%A A141458 _Paul Curtz_, Aug 08 2008