A138413 A bisection of A000957.

0, 0, 2, 18, 186, 2120, 25724, 325878, 4260282, 57048048, 778483932, 10786724388, 151355847012, 2146336125648, 30711521221376, 442862000693438, 6429286894263738, 93891870710425440, 1378379704593824300, 20330047491994213884, 301111732041234778316, 4476705468260134734384, 66784808491631598524136

Offset

0,3

Links

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

Formula

Conjecture: D-finite with recurrence 4*n*(2*n-1)*(7*n-13)*a(n) +(-910*n^3+3489*n^2-4277*n+1680)*a(n-1) +2*(4*n-7)*(7*n-6)*(4*n-5)*a(n-2)=0. Telescoping would provide another recurrence for A000957. - R. J. Mathar, Jun 26 2020

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):
seq(a(n), n=0..25);  # Alois P. Heinz, Apr 26 2023

Prog

(Python)
from itertools import count, islice
def A138413_gen(): # generator of terms
    yield from (0, 0)
    a, c = 0, 1
    for n in count(1, 2):
        a = (c:=c*((n<<2)+2)//(n+2))-a>>1
        yield (a:=(c:=c*((n+1<<2)+2)//(n+3))-a>>1)
A138413_list = list(islice(A138413_gen(), 20)) # Chai Wah Wu, Apr 26 2023

Crossrefs

Cf. A000957, A138414.

Sequence in context: A129627 A279860 A362731 * A066274 A052623 A362992

Adjacent sequences: A138410 A138411 A138412 * A138414 A138415 A138416

Keyword

nonn,easy

Author

N. J. A. Sloane, May 08 2008

Status

approved