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.
-
f:= n -> doublefactorial(2*n+1) mod doublefactorial(2*n):
map(f, [$1..40]); # Robert Israel, Jan 28 2019
-
Mod[#[[2]],#[[1]]]&/@Partition[Range[2,42]!!,2] (* Harvey P. Dale, May 29 2025 *)
-
o=e=1
for n in range(2, 99, 2):
o*=n+1
e*=n
print(o%e, end=', ')
A232620
Numbers k such that (2k)!! mod (2k-1)!! is greater than (2k+2)!! mod (2k+1)!!.
Original entry on oeis.org
4, 615, 9090, 11011
Offset: 1
4 is in the sequence because A232618(4) > A232618(5).
-
o=e=1 # odd, even
prev=0
for n in range(1,1000000000,2):
o*=n
e*=n+1
cur = e%o
if prev>cur: print(str(n//2), end=', ')
prev=cur
A232701
a(n) = (2*n-1)!! mod n!, where double factorial is A006882.
Original entry on oeis.org
0, 1, 3, 9, 105, 315, 4095, 11025, 348705, 1545075, 17931375, 93087225, 3764185425, 45589819275, 1060569885375, 15877899662625, 900941666625, 5722531807867875, 90088576482279375, 1688777976676415625, 18148954872023600625, 320586579951629866875, 11054393914490520969375
Offset: 1
a(4) = 1*3*5*7 mod (1*2*3*4) = 105 mod 24 = 9.
-
o = 1; Reap[For[n = 1, n <= 99, n += 2, o *= n; m = Mod[o, (Quotient[n, 2] + 1)!]; Sow[m]]][[2, 1]] (* Jean-François Alcover, Oct 05 2017, translated from Alex Ratushnyak's Python code *)
-
import math
o=1
for n in range(1,99,2):
o*=n
print(o % math.factorial(n//2+1), 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.
-
o=e=1
for n in range(2, 99, 2):
o*=n+1
e*=n
print(o+e, end=', ')
Showing 1-4 of 4 results.
Comments