A273983 - OEIS

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

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OFFSET

1,2

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

PROG

(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))