A202941 For n>=0, let n!^(2)=A202367(n+1) and, for 0<=m<=n, C^(2)(n,m)=n!^(2)/(m!^(2)*(n-m)!^(2)). The sequence gives triangle of numbers C^(2)(n,m) with rows of length n+1.

1, 1, 1, 1, 10, 1, 1, 21, 21, 1, 1, 20, 42, 20, 1, 1, 11, 22, 22, 11, 1, 1, 2730, 3003, 2860, 3003, 2730, 1, 1, 1, 273, 143, 143, 273, 1, 1

Offset

0,5

Comments

Conjecture. If p is an odd prime, then the ((p-1)/2))-th row contains two 1's and (p-3)/2 numbers multiple of p.

See also comments in A175669 and A202917.

Links

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

Formula

If conjectural formula in A202367 is true, then A007814(C^(2)(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....10.....1
.3..|..1....21 ...21.....1
.4..|..1....20....42....20.....1
.5..|..1....11....22....22....11.....1
.6..|..1..2730..3003..2860..3003..2730.....1
.7..|..1.....1...273...143...143...273.....1.....1
.8..|

Crossrefs

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

Sequence in context: A168620 A143683 A146773 * A166341 A113280 A159041

Adjacent sequences: A202938 A202939 A202940 * A202942 A202943 A202944

Keyword

nonn,tabl

Author

Vladimir Shevelev and Peter J. C. Moses, Dec 26 2011

Status

approved