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A141458
a(n) = A000111(2n) + A000111(2n+1).
1
2, 3, 21, 333, 9321, 404313, 25071021, 2103118293, 229256855121, 31493764788273, 5321869241361621, 1084772760899990253, 262436014353765070521, 74338674113237083780233, 24371443829213227706941821, 9155506650374192400724494213, 3906927095300068860534174415521
OFFSET
0,1
LINKS
FORMULA
a(2n) == 21 (mod 100), n>0.
a(n) = (2n)! * [x^(2n)] sec(x) + sec(x)^2. - Ira M. Gessel, Apr 18 2013
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 *)
PROG
(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
CROSSREFS
Cf. A000111.
Sequence in context: A328734 A296254 A114749 * A080670 A288532 A073647
KEYWORD
nonn
AUTHOR
Paul Curtz, Aug 08 2008
STATUS
approved