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

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

Author

Clark Kimberling

Keywords

• nonn

Links

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

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