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

0,2

Links

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

Formula

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

Mathematica

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

Prog

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

Crossrefs

Cf. A001222, A022559.

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

Sequence in context: A375712 A274341 A164888 * A023979 A319280 A214975

Adjacent sequences: A023982 A023983 A023984 * A023986 A023987 A023988

Keyword

nonn

Author

Clark Kimberling

Extensions

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

Status

approved