A023985 Sum of exponents in prime-power factorization of multinomial coefficient M(6n,2n,2n,2n).

0, 4, 7, 11, 12, 14, 18, 22, 19, 22, 25, 30, 30, 32, 31, 34, 33, 36, 34, 40, 39, 43, 49, 50, 49, 49, 51, 54, 51, 54, 57, 63, 56, 56, 60, 63, 61, 67, 67, 68, 67, 67, 70, 77, 76, 77, 80, 83, 78, 81, 79, 84, 85, 84, 88, 93, 89, 93, 95, 99, 95, 99, 102, 100, 94, 95, 98, 102, 98, 101, 105, 109, 104

Offset: 0

Author

Clark Kimberling

Keywords

• nonn

Links

• Amiram Eldar, Table of n, a(n) for n = 0..10000

Crossrefs

Cf. A001222, A022559.

Cf. A023978, A023979, A023980, A023981, A023982, A023983, A023984, A023986, A023987, A023990, A023991, A023992, A023993.

Programs

Mathematica

a[n_] := PrimeOmega[Multinomial[2*n, 2*n, 2*n]]; Array[a, 100, 0] (* Amiram Eldar, Jun 11 2025 *)

PARI

a(n) = bigomega((6*n)! / ((2*n)!)^3); \\ Amiram Eldar, Jun 11 2025

Formula

a(n) = A022559(6*n) - 3*A022559(2*n). - Amiram Eldar, Jun 11 2025

Extensions

Offset changed to 0 and a(0) prepended by Amiram Eldar, Jun 11 2025