A273889 a(n) = ((4n-3)!! + (4n-2)!!) / (4n-1).

1, 9, 435, 52017, 11592315, 4152126825, 2182133628675, 1581940549814625, 1512952069890336075, 1845586177840605209625, 2796710279417971723681875, 5153962250373844341910100625, 11351091844757135191108560046875, 29444207228221006416048397134215625, 88848552445321896564985597922269171875

Offset

1,2

Links

Hong-Chang Wang, Table of n, a(n) for n = 1..100

Brian Cheung, Proof that (4n-1) divides (4n-3)!! + (4n-2)!!

Hong-Chang Wang, Bridan's blog (in Chinese)

Example

a(1) = (1 + 2)/3 = 1;
a(2) = (1*3*5 + 2*4*6)/7 = 9;
a(3) = (1*3*5*7*9 + 2*4*6*8*10)/11 = 435.

Mathematica

B[n_, k_] := (Product[k (i - 1) + 1, {i, 2 n - 1}] + Product[k (i - 1) + 2, {i, 2 n - 1}])/(2 k (n - 1) + 3); Table[B[n, 2], {n, 15}] (* Michael De Vlieger, Jun 10 2016 *)
Table[((4n-3)!!+(4n-2)!!)/(4n-1), {n, 20}] (* Harvey P. Dale, Mar 08 2018 *)

Prog

(Python)
for n in range(1, 101):
    if n == 1:
        a = 1
        b = 2
    else:
        a = a*(4*n-5)*(4*n-3)
        b = b*(4*n-4)*(4*n-2)
    c = (a+b)/(4*n-1)
    print(str(n)+" "+str(c))

Crossrefs

Cf. A000165, A001147, A006882, A004767, A103639.

Sequence in context: A092813 A242280 A266294 * A167720 A287102 A173954

Adjacent sequences: A273886 A273887 A273888 * A273890 A273891 A273892

Keyword

nonn

Author

Jiangshan Sun, Brian Cheung, Jason Y.S. Chiu, Hong-Chang Wang, Jun 02 2016

Status

approved