|
|
A248332
|
|
Square array read by antidiagonals downwards: super Patalan numbers of order 8.
|
|
3
|
|
|
1, 8, 56, 288, 224, 3360, 13056, 5376, 8960, 206080, 652800, 182784, 161280, 412160, 12776960, 34467840, 7311360, 4386816, 5935104, 20443136, 797282304, 1884241920, 321699840, 146227200, 134529024, 245317632, 1063043072, 49963024384, 105517547520, 15073935360, 5514854400, 3843686400
(list;
table;
graph;
refs;
listen;
history;
text;
internal format)
|
|
|
OFFSET
|
0,2
|
|
COMMENTS
|
Generalization of super Catalan numbers, A068555, based on Patalan numbers of order 8, A025753.
|
|
LINKS
|
|
|
FORMULA
|
a(0,0)=1, a(n,k) = a(n-1,k)*(64*n-8)/(n+k), a(n,k) = a(n,k-1)*(64*k-56)/(n+k).
G.f.: ((x/(1-64*x)^(7/8)+y/(1-64*y)^(1/8))/(x+y-64*x*y).
a(n,k) = (-1)^k*64^(n+k)*binomial(n-1/8,n+k).
|
|
EXAMPLE
|
a(0..4,0..4) is
1 8 288 13056 652800
56 224 5376 182784 7311360
3360 8960 161280 4386816 146227200
206080 412160 5935104 134529024 3843686400
12776960 20443136 245317632 4766171136 119154278400
|
|
PROG
|
(PARI) matrix(5, 5, nn, kk, n=nn-1; k=kk-1; (-1)^k*64^(n+k)*binomial(n-1/8, n+k)) \\ Michel Marcus, Oct 09 2014
|
|
CROSSREFS
|
|
|
KEYWORD
|
|
|
AUTHOR
|
|
|
STATUS
|
approved
|
|
|
|