A263070 Number of lattice paths from {n}^10 to {0}^10 using steps that decrement one or more components by one.

1, 102247563, 1843200116875263613, 93777824804632275267836362863, 7581761490297442738124283591348762605121, 797656368265147949572521540584234236944835806750363, 99479717242433942914309980793245660313479486272546475327799069

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

Column k=10 of A262809.

Programs

Mathematica

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

Formula

a(n) ~ sqrt(c) * d^n / (Pi*n)^(9/2), where d = 275651917450.670923828699577660562035773700532729... and c = 0.02031773288889520997973589484779079409621454... . - Vaclav Kotesovec, Mar 23 2016