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
KEYWORD
nonn
AUTHOR
STATUS
approved