A067347 Square array read by antidiagonals: T(n,k)=(T(n,k-1)*n^2-Catalan(k-1)*n)/(n-1) with a(n,0)=1 and a(1,k)=Catalan(k) where Catalan(k)=C(2k,k)/(k+1)=A000108(k).

1, 0, 1, 0, 1, 1, 0, 2, 2, 1, 0, 5, 6, 3, 1, 0, 14, 20, 12, 4, 1, 0, 42, 70, 51, 20, 5, 1, 0, 132, 252, 222, 104, 30, 6, 1, 0, 429, 924, 978, 548, 185, 42, 7, 1, 0, 1430, 3432, 4338, 2904, 1150, 300, 56, 8, 1, 0, 4862, 12870, 19323, 15432, 7170, 2154, 455, 72, 9, 1, 0, 16796

Offset: 0

Author

Henry Bottomley, Jan 16 2002

Keywords

• nonn
• tabl

Examples

			Array begins
1 0 0 0 0 0 0 0 ... k=0
1 1 2 5 14 42 132 429 ... k=1
1 2 6 20 70 252 924 3432 ... k=2
1 3 12 51 222 978 4338 19323 ... k=3
		

Crossrefs

Rows give A000007, A000108, A000984, A007854, A076035, A076036. Columns give A000012, A001700, A002378, A062158.

Formula

T(n, k) =A067345(n, k)*n =A067346(n, k)*n/(n-1)