A023983 Sum of exponents in prime-power factorization of multinomial coefficient M(5n;2n,2n,n).

0, 3, 6, 8, 10, 12, 14, 19, 17, 18, 21, 24, 24, 29, 27, 29, 27, 31, 29, 33, 35, 37, 39, 41, 40, 40, 45, 45, 43, 48, 48, 54, 46, 48, 51, 52, 51, 56, 57, 59, 58, 57, 60, 61, 62, 65, 64, 69, 63, 68, 66, 69, 74, 76, 74, 78, 75, 76, 81, 82, 81, 85, 87, 83, 77, 81, 82, 84, 81, 87, 86, 93, 87, 91, 92, 93, 96

Offset: 0

Author

Clark Kimberling

Keywords

• nonn

Links

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

Crossrefs

Cf. A001222, A001459, A022559.

Cf. A023978, A023979, A023980, A023981, A023982, A023984, A023985, A023986, A023987, A023990, A023991, A023992, A023993.

Programs

Mathematica

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

PARI

a(n) = bigomega((5*n)! / ((2*n)!^2*n!)); \\ Amiram Eldar, Jun 11 2025

Formula

From Amiram Eldar, Jun 11 2025: (Start)

a(n) = A001222(A001459(n)).

a(n) = A022559(5*n) - 2*A022559(2*n) - A022559(n). (End)

Extensions

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