A263068 Number of lattice paths from {n}^8 to {0}^8 using steps that decrement one or more components by one.

1, 545835, 14623910308237, 874531783382503604463, 74896283763383392805211587121, 7868854300758955660834916406038038395, 943457762940832669626002608045124343895474045, 124069835911824710311393852646151897334844371419287295

Offset

0,2

Links

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

Formula

a(n) ~ sqrt(c) * d^n / (Pi*n)^(7/2), where d = 222082591.60172024210290001176855308841678706675284935653958249024021852... is the root of the equation 1 - 24*d - 102692*d^2 - 9298344*d^3 + 536208070*d^4 - 7106080680*d^5 - 1688209700*d^6 - 222082584*d^7 + d^8 = 0 and c = 0.065002105820899877029614597832047121767362853... . - Vaclav Kotesovec, Mar 23 2016

Mathematica

With[{k = 8}, 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 *)

Crossrefs

Column k=8 of A262809.

Sequence in context: A320622 A218098 A293585 * A237729 A251035 A236827

Adjacent sequences: A263065 A263066 A263067 * A263069 A263070 A263071

Keyword

nonn

Author

Alois P. Heinz, Oct 08 2015

Status

approved