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

2, 3, 21, 333, 9321, 404313, 25071021, 2103118293, 229256855121, 31493764788273, 5321869241361621, 1084772760899990253, 262436014353765070521, 74338674113237083780233, 24371443829213227706941821, 9155506650374192400724494213, 3906927095300068860534174415521

Offset: 0

Author

Paul Curtz, Aug 08 2008

Keywords

• nonn

Links

• Alois P. Heinz, Table of n, a(n) for n = 0..100

Crossrefs

Cf. A000111.

Programs

Maple

A000111 := proc(n) if n = 0 then 1; else 2^n*abs(euler(n, 1/2)+euler(n, 1) ); end if; end proc:
A141458 := proc(n) A000111(2*n)+A000111(2*n+1) ; end proc: # R. J. Mathar, Jul 07 2011

Mathematica

terms = 20;
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 *)

Python

from itertools import accumulate, islice
def A141458_gen(): # generator of terms
    yield 2
    blist = (0,1)
    while True:
        yield (blist := tuple(accumulate(reversed(blist),initial=0)))[-1] + (blist := tuple(accumulate(reversed(blist),initial=0)))[-1]
A141458_list = list(islice(A141458_gen(),30)) # Chai Wah Wu, Apr 17 2023

Formula

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

a(n) = (2n)! * [x^(2n)] sec(x) + sec(x)^2. - Ira M. Gessel, Apr 18 2013