A138414 A bisection of A000957.

1, 1, 6, 57, 622, 7338, 91144, 1174281, 15548694, 210295326, 2892818244, 40347919626, 569274150156, 8110508473252, 116518215264492, 1686062250699433, 24552388991392230, 359526085719652662, 5290709340633314596, 78201907647506243758, 1160507655117628665252, 17283862221822154612428, 258257655550682547281952

Offset: 0

Author

N. J. A. Sloane, May 08 2008

Keywords

• nonn
• easy

Crossrefs

Cf. A000957, A138413.

Programs

Maple

b:= proc(n) option remember; `if`(n<3, n*(2-n),
      ((7*n-12)*b(n-1)+(4*n-6)*b(n-2))/(2*n))
    end:
a:= n-> b(2*n+1):
seq(a(n), n=0..25);  # Alois P. Heinz, Apr 26 2023

PARI

x='x+O('x^100);  v=Vec((1-sqrt(1-4*x))/(3-sqrt(1-4*x)));
vector(#v\2,n,v[2*n-1]) /* show terms */

Python

from itertools import count, islice
def A138414_gen(): # generator of terms
    yield 1
    a, c = 0, 1
    for n in count(1,2):
        yield (a:=(c:=c*((n<<2)+2)//(n+2))-a>>1)
        a=(c:=c*((n+1<<2)+2)//(n+3))-a>>1
A138414_list = list(islice(A138414_gen(),20)) # Chai Wah Wu, Apr 26 2023

Formula

a(n) = A000957(2*n+1).