A263061 Number of lattice paths from {5}^n to {0}^n using steps that decrement one or more components by one.

1, 1, 1683, 32193253, 3147728203035, 1050740615666453461, 939073157252309315848923, 1909946024633189859690880523893, 7868854300758955660834916406038038395, 60169662022264019813634467045726478557798101, 797656368265147949572521540584234236944835806750363

Offset

0,3

Links

Alois P. Heinz, Table of n, a(n) for n = 0..100

Formula

From Vaclav Kotesovec, Mar 23 2016: (Start)

a(n) ~ 5^(4*n+1/2) * n!^5 / (Pi^2 * n^2 * 2^(3*n+5) * 3^n * (log(2))^(5*n+1)).

a(n) ~ sqrt(Pi) * 5^(4*n+1/2) * n^(5*n+1/2) / (2^(3*n+5/2) * 3^n * exp(5*n) * (log(2))^(5*n+1)).

(End)

Mathematica

With[{r = 5}, 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 *)

Crossrefs

Row n=5 of A262809.

Sequence in context: A206671 A205515 A335338 * A281062 A020241 A065903

Adjacent sequences: A263058 A263059 A263060 * A263062 A263063 A263064

Keyword

nonn

Author

Alois P. Heinz, Oct 08 2015

Status

approved