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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 * A336906 A334332 A068552 Adjacent sequences:  A248329 A248330 A248331 * A248333 A248334 A248335 KEYWORD nonn,tabl,easy AUTHOR Tom Richardson, Oct 04 2014 STATUS approved

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Last modified January 27 10:14 EST 2022. Contains 350607 sequences. (Running on oeis4.)