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

0,2

Comments

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

Links

Table of n, a(n) for n=0..31.

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

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).

Example

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

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

Adjacent sequences: A248329 A248330 A248331 * A248333 A248334 A248335

Keyword

nonn,tabl,easy

Author

Tom Richardson, Oct 04 2014

Status

approved