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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
Thomas M. Richardson, The Super Patalan Numbers, arXiv:1410.5880 [math.CO], 2014.
Thomas M. Richardson, The Super Patalan Numbers, Journal of Integer Sequences, Vol. 18 (2015), Article 15.3.3.
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
Cf. A068555, A025753, A034977 (first row), A216704 (first column), A248324, A248325, A248326, A248328, A248329.
Sequence in context: A168013 A003210 A135417 * A354548 A336906 A334332
KEYWORD
nonn,tabl,easy
AUTHOR
Tom Richardson, Oct 04 2014
STATUS
approved

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Last modified March 28 22:04 EDT 2024. Contains 371254 sequences. (Running on oeis4.)