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.

Previous Showing 11-13 of 13 results.

A023990 Sum of exponents of primes in multinomial coefficient M(4n; 2n,n,n) - sum of exponents of primes in M(3n; n,n,n).

Original entry on oeis.org

0, 1, 1, 1, 2, 2, 1, 3, 3, 4, 4, 1, 2, 4, 3, 3, 5, 4, 4, 3, 4, 7, 4, 4, 5, 7, 5, 4, 5, 5, 6, 6, 7, 7, 9, 7, 9, 11, 8, 9, 9, 9, 8, 6, 7, 7, 6, 6, 8, 9, 8, 8, 9, 10, 7, 8, 9, 10, 11, 7, 8, 11, 11, 10, 12, 13, 13, 12, 11, 14, 12, 11, 13, 14, 12, 12, 14, 14, 13, 14, 14, 15, 15, 13, 14, 14, 11, 10, 13, 12, 13, 13, 12, 15
Offset: 0

Views

Author

Clark Kimberling

Keywords

Links

Crossrefs

Cf. A001222, A000897, A006480, A022559.
Cf. A023978, A023979, A023980, A023981, A023982, A023983, A023984, A023985, A023986, A023987, A023991, A023992, A023993.

Programs

  • Mathematica
    a[n_] := PrimeOmega[Multinomial[2*n, n, n]] - PrimeOmega[Multinomial[n, n, n]]; Array[a, 100, 0] (* Amiram Eldar, Jun 11 2025 *)
  • PARI
    a(n) = bigomega((4*n)!/((2*n)!*n!^2)) - bigomega((3*n)!/(n!^3)); \\ Amiram Eldar, Jun 11 2025

Formula

From Amiram Eldar, Jun 11 2025: (Start)
a(n) = A023980(n) - A023978(n) = A001222(A000897(n)) - A001222(A006480(n)).
a(n) = A022559(4*n) + 2*A022559(n) - A022559(2*n) - A022559(3*n). (End)

Extensions

Name clarified, offset changed to 0 and a(0) prepended by Amiram Eldar, Jun 11 2025

A023992 Sum of exponents of primes in multinomial coefficient M(4n; n+2,2n,n-2).

Original entry on oeis.org

3, 7, 9, 11, 11, 15, 15, 19, 18, 19, 21, 24, 22, 25, 26, 28, 26, 29, 29, 34, 33, 34, 36, 38, 35, 38, 38, 39, 38, 41, 42, 44, 43, 44, 46, 49, 45, 50, 50, 52, 51, 54, 55, 58, 55, 56, 58, 61, 57, 60, 60, 61, 60, 63, 62, 66, 64, 66, 67, 71, 68, 70, 72, 73, 70, 72, 70, 76, 74, 75, 77, 79, 76
Offset: 2

Views

Author

Clark Kimberling

Keywords

Links

Crossrefs

Cf. A001222, A022559.
Cf. A023978, A023979, A023980, A023981, A023982, A023983, A023984, A023985, A023986, A023987, A023990, A023991, A023993.

Programs

  • Mathematica
    a[n_] := PrimeOmega[Multinomial[2*n, n+2, n-2]]; Array[a, 100] (* Amiram Eldar, Jun 11 2025 *)
  • PARI
    a(n) = bigomega((4*n)! / ((2*n)!*(n-2)!*(n+2)!)); \\ Amiram Eldar, Jun 11 2025

Formula

a(n) = A022559(4*n) - A022559(2*n) - A022559(n+2) - A022559(n-2). - Amiram Eldar, Jun 11 2025

Extensions

Missing a(1)=1 inserted by Sean A. Irvine, Jun 17 2019
Offset changed to 2 and a(1) removed by Amiram Eldar, Jun 11 2025

A023993 Sum of exponents of primes in multinomial coefficient M(3n; n+2,n-1,n-1).

Original entry on oeis.org

0, 3, 6, 8, 8, 11, 11, 14, 14, 14, 17, 21, 18, 20, 22, 23, 21, 24, 24, 27, 26, 29, 29, 34, 29, 30, 35, 33, 32, 34, 33, 39, 34, 34, 37, 39, 35, 38, 41, 43, 40, 45, 46, 50, 51, 48, 49, 54, 49, 50, 51, 52, 49, 56, 53, 55, 54, 53, 58, 62, 57, 58, 61, 63, 56, 58, 58, 61, 61, 63, 62, 68, 61, 65, 70
Offset: 1

Views

Author

Clark Kimberling

Keywords

Links

Crossrefs

Cf. A001222, A022559.
Cf. A023978, A023979, A023980, A023981, A023982, A023983, A023984, A023985, A023986, A023987, A023990, A023991, A023992.

Programs

  • Mathematica
    a[n_] := PrimeOmega[Multinomial[n + 2, n - 1, n - 1]]; Array[a, 100] (* Amiram Eldar, Jun 11 2025 *)
  • PARI
    a(n) = bigomega((3*n)! / ((n+2)!*(n-1)!^2)); \\ Amiram Eldar, Jun 11 2025

Formula

a(n) = A022559(3*n) - A022559(n+2) - 2*A022559(n-1). - Amiram Eldar, Jun 11 2025
Previous Showing 11-13 of 13 results.

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