A023991 Sum of exponents of primes in multinomial coefficient M(3n; n+1,n,n-1).

1, 4, 6, 8, 8, 12, 12, 13, 13, 15, 17, 20, 19, 22, 21, 22, 21, 24, 25, 26, 25, 31, 30, 32, 30, 31, 33, 33, 32, 36, 34, 36, 34, 36, 36, 37, 36, 40, 40, 42, 40, 45, 48, 49, 49, 51, 50, 52, 49, 50, 50, 53, 50, 56, 53, 53, 53, 55, 58, 60, 59, 62, 60, 60, 55, 58, 59, 61, 60, 65, 62, 65, 63, 66, 69, 68

Offset: 1

Author

Clark Kimberling

Keywords

• nonn

Links

• Amiram Eldar, Table of n, a(n) for n = 1..10000

Crossrefs

Cf. A001222, A022559, A023978, A076191, A248707.

Cf. A023978, A023979, A023980, A023981, A023982, A023983, A023984, A023985, A023986, A023987, A023990, A023992, A023993.

Programs

Mathematica

a[n_] := PrimeOmega[Multinomial[n+1, n, n-1]]; Array[a, 100] (* Amiram Eldar, Jun 11 2025 *)

PARI

a(n) = bigomega((3*n)! / ((n-1)!*n!*(n+1)!)); \\ Amiram Eldar, Jun 11 2025

Formula

From Amiram Eldar, Jun 11 2025: (Start)

a(n) = A001222(A248707(n)).

a(n) = A022559(3*n) - A022559(n-1) - A022559(n) - A022559(n+1) = A022559(3*n) - 3*A022559(n) - A001222(n+1) + A001222(n) = A023978(n) - A076191(n). (End)