A232618
a(n) = (2n)!! mod (2n-1)!! where k!! = A006882(k).
Original entry on oeis.org
0, 2, 3, 69, 60, 4500, 104580, 186795, 13497435, 442245825, 13003053525, 64585694250, 3576632909850, 147580842959550, 5708173568847750, 27904470362393625, 2292043480058957625, 126842184377462428875, 6371504674680470700375, 312265748715684068930625
Offset: 1
a(3) = A006882(6) mod A006882(5) = 2*4*6 mod 1*3*5 = 48 mod 15 = 3.
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Table[Mod[(2n)!!,(2n-1)!!],{n,20}] (* Harvey P. Dale, Sep 23 2020 *)
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o=e=1
for n in range(1,99,2):
o*=n
e*=n+1
print(str(e%o), end=',')
A306184
a(n) = (2n+1)!! mod (2n)!! where k!! = A006882(k).
Original entry on oeis.org
1, 7, 9, 177, 2715, 42975, 91665, 3493665, 97345395, 2601636975, 70985324025, 57891366225, 9411029102475, 476966861546175, 20499289200014625, 847876038362978625, 35160445175104123875, 1487419121780448231375, 945654757149212735625, 357657177058846280240625
Offset: 1
a(3) = A006882(7) mod A006882(6) = (7*5*3) mod (6*4*2) = 105 mod 48 = 9.
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f:= n -> doublefactorial(2*n+1) mod doublefactorial(2*n):
map(f, [$1..40]); # Robert Israel, Jan 28 2019
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Mod[#[[2]],#[[1]]]&/@Partition[Range[2,42]!!,2] (* Harvey P. Dale, May 29 2025 *)
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o=e=1
for n in range(2, 99, 2):
o*=n+1
e*=n
print(o%e, end=', ')
A306185
a(n) = (2n+1)!! + (2n)!! where k!! = A006882(k).
Original entry on oeis.org
5, 23, 153, 1329, 14235, 181215, 2672145, 44781345, 840523635, 17465201775, 397983749625, 9867844134225, 264469801070475, 7618612476650175, 234748657653134625, 7703855828862818625, 268263758052098683875, 9879138385352252391375, 383608053176023482431625, 15664153113813817068080625
Offset: 1
a(3) = A006882(7) + A006882(6) = (7*5*3) + (6*4*2) = 105 + 48 = 153.
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o=e=1
for n in range(2, 99, 2):
o*=n+1
e*=n
print(o+e, end=', ')
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