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

0,5

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

Links

Table of n, a(n) for n=0..65.

Formula

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

Prog

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

Crossrefs

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

Cf. A108625.

Sequence in context: A183944 A145661 A119258 * A247285 A047969 A047812

Adjacent sequences: A099605 A099606 A099607 * A099609 A099610 A099611

Keyword

nonn,tabl

Author

Michael Somos, Oct 25 2004

Status

approved