A263072 Number of lattice paths from {10}^n to {0}^n using steps that decrement one or more components by one.

1, 1, 8097453, 9850349744182729, 331910222316215755702672557, 134565509066155510620216211257550349401, 399017534874989738901076297624977315332337599285373, 6213239693876579408708842528154872834110410698303331900339282569

Offset: 0

Author

Alois P. Heinz, Oct 08 2015

Keywords

• nonn

Comments

In general, row r > 0 of A262809 is asymptotic to sqrt(r*Pi) * (r^(r-1)/(r-1)!)^n * n^(r*n+1/2) / (2^(r/2) * exp(r*n) * (log(2))^(r*n+1)). - Vaclav Kotesovec, Mar 23 2016

Links

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

Crossrefs

Row n=10 of A262809.

Programs

Mathematica

With[{r = 10}, 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(10*Pi) * (10^9/9!)^n * n^(10*n+1/2) / (32 * exp(10*n) * (log(2))^(10*n+1)). - Vaclav Kotesovec, Mar 23 2016