A203484 - OEIS

A203484

For n>=0, let n!^(3) = A202368(n+1) and, for 0<=m<=n, C^(3)(n,m) = n!^(3)/(m!^(3)*(n-m)!^(3)). The sequence gives triangle of numbers C^(3)(n,m) with rows of length n+1.

1, 1, 1, 1, 42, 1, 1, 5, 5, 1, 1, 1092, 130, 1092, 1, 1, 1, 26, 26, 1, 1, 1, 11970, 285, 62244, 285, 11970, 1, 1, 11, 3135, 627, 627, 3135, 11, 1

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OFFSET

0,5

COMMENTS

Conjecture. If p is prime of the form 3*k+1, then the k-th row contains two 1's and k-1 numbers multiple of p; if p is prime of the form 3*k+2, then the (2*k+1)-th row contains two 1's and 2*k numbers multiple of p.

LINKS

Table of n, a(n) for n=0..35.

FORMULA

Conjecture. A007814(C^(3)(n,m)) = A007814(C(n,m)).

EXAMPLE

Triangle begins

n/m.|..0.....1.....2.....3.....4.....5.....6.....7

==================================================

.0..|..1

.1..|..1......1

.2..|..1.....42.....1

.3..|..1......5 ....5......1