The On-Line Encyclopedia of Integer Sequences (OEIS)

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A263072

Number of lattice paths from {10}^n to {0}^n using steps that decrement one or more components by one.
(history; published version)

#9 by Vaclav Kotesovec at Wed Mar 23 04:54:36 EDT 2016

STATUS

editing

approved

#8 by Vaclav Kotesovec at Wed Mar 23 04:42:56 EDT 2016

COMMENTS

In general, row r > 0 of A262809 is asymptotic to sqrt(r*Pi) * (r^(r-1)/(r-1)!)^n * n^(r*n+1/2) / (2^(r/2) * exp(r*n) * (log(2))^(r*n+1)). - Vaclav Kotesovec, Mar 23 2016

#7 by Vaclav Kotesovec at Wed Mar 23 04:42:17 EDT 2016

FORMULA

a(n) ~ sqrt(10*Pi) * (10^9/9!)^n * n^(10*n+1/2) / (32 * exp(10*n) * (log(2))^(10*n+1)). - Vaclav Kotesovec, Mar 23 2016

STATUS

approved

editing

#6 by Vaclav Kotesovec at Tue Mar 22 19:27:45 EDT 2016

STATUS

editing

approved

#5 by Vaclav Kotesovec at Tue Mar 22 18:38:43 EDT 2016

MATHEMATICA

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

STATUS

approved

editing

#4 by Alois P. Heinz at Thu Oct 08 18:25:25 EDT 2015

STATUS

editing

approved

#3 by Alois P. Heinz at Thu Oct 08 18:25:22 EDT 2015

LINKS

Alois P. Heinz, <a href="/A263072/b263072.txt">Table of n, a(n) for n = 0..50</a>

#2 by Alois P. Heinz at Thu Oct 08 18:00:24 EDT 2015

NAME

allocated for Alois P. Heinz

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

DATA

1, 1, 8097453, 9850349744182729, 331910222316215755702672557, 134565509066155510620216211257550349401, 399017534874989738901076297624977315332337599285373, 6213239693876579408708842528154872834110410698303331900339282569

OFFSET

0,3

CROSSREFS

Row n=10 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