A141458 - OEIS

%I #22 Apr 17 2023 11:05:54

%S 2,3,21,333,9321,404313,25071021,2103118293,229256855121,

%T 31493764788273,5321869241361621,1084772760899990253,

%U 262436014353765070521,74338674113237083780233,24371443829213227706941821,9155506650374192400724494213,3906927095300068860534174415521

%N a(n) = A000111(2n) + A000111(2n+1).

%H Alois P. Heinz, <a href="/A141458/b141458.txt">Table of n, a(n) for n = 0..100</a>

%F a(2n) == 21 (mod 100), n>0.

%F a(n) = (2n)! * [x^(2n)] sec(x) + sec(x)^2. - _Ira M. Gessel_, Apr 18 2013

%p 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 := proc(n) A000111(2*n)+A000111(2*n+1) ; end proc: # _R. J. Mathar_, Jul 07 2011

%t terms = 20;

%t 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 (Python)

%o from itertools import accumulate, islice

%o def A141458_gen(): # generator of terms

%o     yield 2

%o     blist = (0,1)

%o     while True:

%o         yield (blist := tuple(accumulate(reversed(blist),initial=0)))[-1] + (blist := tuple(accumulate(reversed(blist),initial=0)))[-1]

%o A141458_list = list(islice(A141458_gen(),30)) # _Chai Wah Wu_, Apr 17 2023

%Y Cf. A000111.

%K nonn

%O 0,1

%A _Paul Curtz_, Aug 08 2008