A248332 Square array read by antidiagonals downwards: super Patalan numbers of order 8.

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

Offset: 0

Author

Tom Richardson, Oct 04 2014

Keywords

• nonn
• tabl
• easy

Comments

Generalization of super Catalan numbers, A068555, based on Patalan numbers of order 8, A025753.

Examples

			T(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
		

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.

Crossrefs

Cf. A068555, A025753, A034977 (first row), A216704 (first column), A248324, A248325, A248326, A248328, A248329.

Programs

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

Formula

T(0,0)=1, T(n,k) = T(n-1,k)*(64*n-8)/(n+k), T(n,k) = T(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).

T(n,k) = (-1)^k*64^(n+k)*binomial(n-1/8,n+k).