A023979 Sum of exponents in prime-power factorization of multinomial coefficient M(4n; n,n,n,n).

0, 4, 7, 11, 12, 16, 17, 23, 21, 23, 24, 28, 27, 33, 36, 37, 33, 38, 37, 42, 41, 44, 46, 52, 48, 51, 52, 51, 50, 55, 55, 60, 55, 57, 61, 62, 58, 64, 66, 70, 65, 72, 71, 78, 78, 76, 78, 84, 79, 81, 80, 82, 82, 88, 84, 86, 82, 85, 88, 94, 90, 98, 102, 102, 93, 95, 94, 100, 100, 104, 103, 107, 102

Offset: 0

Author

Clark Kimberling

Keywords

• nonn

Links

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

Crossrefs

Cf. A001222, A008977, A022559.

Cf. A023978, A023980, A023981, A023982, A023983, A023984, A023985, A023986, A023987, A023990, A023991, A023992, A023993.

Programs

Mathematica

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

PARI

a(n) = bigomega((4*n)! / n!^4); \\ Amiram Eldar, Jun 11 2025

Formula

From Amiram Eldar, Jun 11 2025: (Start)

a(n) = A001222(A008977(n)).

a(n) = A022559(4*n) - 4*A022559(n). (End)

Extensions

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