cp's OEIS Frontend

This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.

Showing 1-4 of 4 results.

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

Views

Author

Alex Ratushnyak, Jan 27 2019

Keywords

Comments

a(n) is divisible by A049606(n). - Robert Israel, Jan 28 2019

Examples

			a(3) = A006882(7) mod A006882(6) = (7*5*3) mod (6*4*2) = 105 mod 48 = 9.
		

Crossrefs

Programs

  • Maple
    f:= n -> doublefactorial(2*n+1) mod doublefactorial(2*n):
    map(f, [$1..40]); # Robert Israel, Jan 28 2019
  • Mathematica
    Mod[#[[2]],#[[1]]]&/@Partition[Range[2,42]!!,2] (* Harvey P. Dale, May 29 2025 *)
  • Python
    o=e=1
    for n in range(2, 99, 2):
      o*=n+1
      e*=n
      print(o%e, end=', ')

Formula

a(n) = A006882(2*n+1) mod A006882(2*n).

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

Views

Author

Alex Ratushnyak, Nov 27 2013

Keywords

Comments

Numbers k such that A232618(k) > A232618(k+1).
a(5) > 10 * 2^20.

Examples

			4 is in the sequence because A232618(4) > A232618(5).
		

Crossrefs

Programs

  • Python
    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

Views

Author

Alex Ratushnyak, Nov 28 2013

Keywords

Comments

(2n-1)!! is the product of first n odd numbers.

Examples

			a(4) = 1*3*5*7 mod (1*2*3*4) = 105 mod 24 = 9.
		

Crossrefs

Cf. A006882, A232618, A024502 (floor((2*n-1)!! / n!)).

Programs

  • Mathematica
    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 *)
  • Python
    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

Views

Author

Alex Ratushnyak, Jan 27 2019

Keywords

Examples

			a(3) = A006882(7) + A006882(6) = (7*5*3) + (6*4*2) = 105 + 48 = 153.
		

Crossrefs

Programs

  • Python
    o=e=1
    for n in range(2, 99, 2):
      o*=n+1
      e*=n
      print(o+e, end=', ')

Formula

a(n) = A006882(2*n+1) + A006882(2*n).
Showing 1-4 of 4 results.