A023981 Sum of exponents in prime-power factorization of multinomial coefficient M(5n; n,n,n,n,n).

0, 5, 10, 14, 16, 22, 24, 31, 29, 30, 33, 40, 38, 47, 49, 51, 45, 53, 51, 57, 59, 61, 63, 71, 66, 68, 75, 73, 71, 80, 78, 86, 76, 80, 83, 86, 81, 88, 93, 97, 92, 99, 100, 105, 106, 107, 108, 117, 107, 112, 112, 115, 118, 126, 120, 124, 119, 120, 127, 134, 131, 139, 143, 141, 127, 133

Offset: 0

Author

Clark Kimberling

Keywords

• nonn

Links

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

Crossrefs

Cf. A001222, A008978, A022559.

Cf. A023978, A023979, A023980, A023982, A023983, A023984, A023985, A023986, A023987, A023990, A023991, A023992, A023993.

Programs

Mathematica

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

PARI

a(n) = bigomega((5*n)! / n!^5); \\ Amiram Eldar, Jun 11 2025

Formula

From Amiram Eldar, Jun 11 2025: (Start)

a(n) = A001222(A008978(n)).

a(n) = A022559(5*n) - 5*A022559(n). (End)

Extensions

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