A273983 a(n) = ((4*n)!! - (4*n-1)!!)/(4*n+1).

1, 31, 2745, 487935, 145769625, 65830256415, 41892106080825, 35736278004165375, 39370290736153001625, 54420772423242699849375, 92234193751998833171261625, 188098544080793843475953349375, 454418941572893462364414856265625, 1283429428883663190972186961851609375

Offset: 1

Author

Chai Wah Wu, Jun 05 2016

Keywords

• nonn

Comments

Sequence is inspired by A273889. The same argument in A273889 can be used here to prove the expression evaluates to integers.

Links

• Chai Wah Wu, Table of n, a(n) for n = 1..202

Crossrefs

Cf. A273889, A007912.

Programs

Python

doublefac=lambda x:1 if x<2 else x*doublefac(x-2)
for i in range(200):
    print(i,(doublefac(4*i)-doublefac(4*i-1))//(4*i+1))
# Brian Cheung, Jun 15 2016