A102445 Number of prime divisors (counted with multiplicity) of the central trinomial coefficients (A002426).

0, 1, 1, 1, 2, 2, 2, 4, 2, 2, 3, 2, 2, 4, 3, 4, 6, 3, 2, 3, 3, 5, 6, 6, 4, 9, 3, 3, 2, 3, 3, 4, 5, 3, 5, 4, 2, 3, 3, 4, 2, 7, 5, 7, 7, 5, 5, 6, 6, 4, 5, 8, 9, 4, 5, 6, 3, 3, 7, 6, 8, 7, 7, 4, 5, 4, 4, 7, 7, 9, 11, 5, 8, 7, 7, 6, 7, 7, 8, 12, 4, 7, 6, 6, 4, 8, 7, 4, 10, 7, 7, 6, 6, 7, 5, 5, 6, 8, 7, 9, 10, 5, 7

Offset

1,5

Comments

First occurrence of k: 1,2,5,11,8,22,17,42,52,26,89,71,80,....

Links

Amiram Eldar, Table of n, a(n) for n = 1..218

Eric Weisstein's World of Mathematics, Trinomial Coefficient..

Formula

a(n) = A001222(A002426(n)). - Amiram Eldar, Feb 06 2020

Mathematica

bigomega[n_Integer] := Plus @@ Last /@ FactorInteger[n]; tn[n_] := Sum[Binomial[n, k]*Binomial[n - k, k], {k, 0, n/2}]; Table[bigomega[tn[n]], {n, 103}] (* Robert G. Wilson v, Feb 21 2005 *)

Crossrefs

Cf. A001222, A002426.

Sequence in context: A049298 A075016 A279409 * A102430 A160691 A367626

Adjacent sequences: A102442 A102443 A102444 * A102446 A102447 A102448

Keyword

nonn

Author

Jonathan Vos Post, Feb 21 2005

Extensions

Edited and extended by Robert G. Wilson v, Feb 21 2005

Status

approved