A099608 Table of crystal ball sequences for A_n lattices read by antidiagonals.

1, 1, 1, 1, 3, 1, 1, 5, 7, 1, 1, 7, 19, 13, 1, 1, 9, 37, 55, 21, 1, 1, 11, 61, 147, 131, 31, 1, 1, 13, 91, 309, 471, 271, 43, 1, 1, 15, 127, 561, 1251, 1281, 505, 57, 1, 1, 17, 169, 923, 2751, 4251, 3067, 869, 73, 1, 1, 19, 217, 1415, 5321, 11253, 12559, 6637, 1405, 91, 1

Offset: 0

Author

Michael Somos, Oct 25 2004

Keywords

• nonn
• tabl

Comments

Rows (n=0..10) are A000012, A005408, A003215, A005902, A008384, A008386, A008388, A008390, A008392, A008394, A008396.

Row reverse of A108625. - Peter Bala, Jul 18 2008

Crossrefs

T(n, n)=A005258(n), T(2n, n)=A099601(n).

Cf. A108625.

Programs

PARI

T(n,k)=sum(j=0,min(n,k),binomial(n+j,j)*binomial(n,j)*binomial(k,j))

Formula

T(n, k)=hypergeom([n+1, -n, -k], [1, 1], 1).