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

Author

N. J. A. Sloane, May 08 2008

Keywords

• nonn
• easy

Crossrefs

Cf. A000957, A138414.

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

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

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