A263066 Number of lattice paths from {n}^6 to {0}^6 using steps that decrement one or more components by one.

1, 4683, 308682013, 35941784497263, 5402040231378569121, 939073157252309315848923, 179349571255187154941191217629, 36585008462723983824862891403150079, 7835213566547395052871069325808866414849, 1742079663955078309800553960117733249663480043

Offset

0,2

Links

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

Vaclav Kotesovec, Recurrence (of order 6)

Formula

a(n) ~ sqrt(c) * d^n / (Pi*n)^(5/2), where d = 296476.91626442008149098622814984912648229139426918084511... is the root of the equation 1 - 18*d - 5397*d^2 - 123696*d^3 + 321303*d^4 - 296478*d^5 + d^6 = 0 and c = 0.19491147281619801027873171908746401584984116403035035539868... is the root of the equation -1 - 4608*c - 7962624*c^2 - 6341787648*c^3 - 2283043553280*c^4 - 300578991243264*c^5 + 1603087953297408*c^6 = 0. - Vaclav Kotesovec, Mar 23 2016

Mathematica

With[{k = 6}, Table[Sum[Sum[(-1)^i*Binomial[j, i]*Binomial[j - i, n]^k, {i, 0, j}], {j, 0, k*n}], {n, 0, 15}]] (* Vaclav Kotesovec, Mar 22 2016 *)

Crossrefs

Column k=6 of A262809.

Sequence in context: A320620 A218096 A293583 * A252773 A368192 A204073

Adjacent sequences: A263063 A263064 A263065 * A263067 A263068 A263069

Keyword

nonn

Author

Alois P. Heinz, Oct 08 2015

Status

approved