A263063 Number of lattice paths from {8}^n to {0}^n using steps that decrement one or more components by one.

1, 1, 265729, 3776339263873, 756051015055329306625, 1100327453912286201909924526081, 7835213566547395052871069325808866414849, 209691630817770382144439647416526247292909726379393, 17469051230066445323872793284679234619523576313653708533767425

Offset: 0

Author

Alois P. Heinz, Oct 08 2015

Keywords

• nonn

Links

• Alois P. Heinz, Table of n, a(n) for n = 0..50

Crossrefs

Row n=8 of A262809.

Programs

Mathematica

With[{r = 8}, Flatten[{1, Table[Sum[Sum[(-1)^i*Binomial[j, i]*Binomial[j - i, r]^k, {i, 0, j}], {j, 0, k*r}], {k, 1, 10}]}]] (* Vaclav Kotesovec, Mar 22 2016 *)

Formula

a(n) ~ sqrt(8*Pi) * (8^7/7!)^n * n^(8*n+1/2) / (16 * exp(8*n) * (log(2))^(8*n+1)). - Vaclav Kotesovec, Mar 23 2016