A263062 Number of lattice paths from {6}^n to {0}^n using steps that decrement one or more components by one.

1, 1, 8989, 1538743249, 1887593866439485, 10169807398958450670001, 179349571255187154941191217629, 8508048612432263410111274212273801489, 943457762940832669626002608045124343895474045, 220079308019032269943223432841210561656944209845808241

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=6 of A262809.

Programs

Mathematica

With[{r = 6}, Flatten[{1, Table[Sum[Sum[(-1)^i*Binomial[j, i]*Binomial[j - i, r]^k, {i, 0, j}], {j, 0, k*r}], {k, 1, 12}]}]] (* Vaclav Kotesovec, Mar 22 2016 *)

Formula

a(n) ~ sqrt(6*Pi) * (6^5/5!)^n * n^(6*n+1/2) / (8 * exp(6*n) * (log(2))^(6*n+1)). - Vaclav Kotesovec, Mar 23 2016