[seqfan] T(n, k)=Number of nondecreasing arrangements of n numbers in -k..k with sum zero

[Ron Hardin]

This turns out to match a lot of existing sequences:

(new) T(n,k)=Number of nondecreasing arrangements of n numbers in -k..k with sum 
zero

Table starts (offset 1,1)
.1..1...1....1....1.....1.....1......1......1......1.......1.......1.......1
.2..3...4....5....6.....7.....8......9.....10.....11......12......13......14
.2..5...8...13...18....25....32.....41.....50.....61......72......85......98
.3..8..18...33...55....86...126....177....241....318.....410.....519.....645
.3.12..32...73..141...252...414....649....967...1394....1944....2649....3523
.4.18..58..151..338...676..1242...2137...3486...5444....8196...11963...17002
.4.24..94..289..734..1656..3370...6375..11322..19138...30982...48417...73316
.5.33.151..526.1514..3788..8512..17575..33885..61731..107233..178870..288100
.5.43.227..910.2934..8150.20094..45207..94257.184717..343363..610358.1043534
.6.55.338.1514.5448.16660.44916.109583.246448.517971.1028172.1943488.3521260

Column 2 is A001973
Column 3 is A001977
Column 4 is A001981
Diagonal is A109655
Row 3 is A000982(n+1)


 rhhardin at mindspring.com
rhhardin at att.net (either)