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

0,3

Links

Table of n, a(n) for n=0..22.

Formula

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

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

Prog

(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

Crossrefs

Cf. A000957, A138413.

Sequence in context: A371521 A246235 A213105 * A349363 A130565 A124556

Adjacent sequences: A138411 A138412 A138413 * A138415 A138416 A138417

Keyword

nonn,easy

Author

N. J. A. Sloane, May 08 2008

Status

approved