The On-Line Encyclopedia of Integer Sequences (OEIS)

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Number of lattice paths from {n}^8 to {0}^8 using steps that decrement one or more components by one.
(history; published version)

#8 by Vaclav Kotesovec at Wed Mar 23 12:55:58 EDT 2016

STATUS

editing

approved

#7 by Vaclav Kotesovec at Wed Mar 23 12:27:11 EDT 2016

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

STATUS

approved

editing

#6 by Vaclav Kotesovec at Tue Mar 22 19:26:21 EDT 2016

STATUS

editing

approved

#5 by Vaclav Kotesovec at Tue Mar 22 18:23:33 EDT 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 *)

STATUS

approved

editing

#4 by Alois P. Heinz at Fri Oct 09 12:09:40 EDT 2015

STATUS

editing

approved

#3 by Alois P. Heinz at Fri Oct 09 12:09:04 EDT 2015

LINKS

Alois P. Heinz, <a href="/A263068/b263068.txt">Table of n, a(n) for n = 0..50</a>

#2 by Alois P. Heinz at Thu Oct 08 17:47:16 EDT 2015

NAME

allocated for Alois P. Heinz

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

DATA

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

OFFSET

0,2

CROSSREFS

Column k=8 of A262809.

KEYWORD

allocated

nonn

AUTHOR

Alois P. Heinz, Oct 08 2015

STATUS

approved

editing

#1 by Alois P. Heinz at Thu Oct 08 17:32:53 EDT 2015

NAME

allocated for Alois P. Heinz

KEYWORD

allocated

STATUS

approved