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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. 3
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 (list; table; graph; refs; listen; history; text; internal format)
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

.4..|..1...1092...130...1092.....1

.5..|..1......1....26.....26.....1......1

.6..|..1..11970...285..62244...285..11970....1

.7..|..1.....11..3135....627...627...3135...11.....1

.8..|

CROSSREFS

Cf. A175669, A053657, A202339, A202367, A202368, A202369, A202917, A202941.

Sequence in context: A263303 A263288 A216799 * A176920 A037938 A091747

Adjacent sequences:  A203481 A203482 A203483 * A203485 A203486 A203487

KEYWORD

nonn,tabl

AUTHOR

Vladimir Shevelev and Peter J. C. Moses, Jan 02 2012

STATUS

approved

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Last modified August 20 10:17 EDT 2019. Contains 326149 sequences. (Running on oeis4.)