A248325 Square array read by antidiagonals downwards: super Patalan numbers of order 4.

1, 4, 12, 40, 24, 168, 480, 160, 224, 2464, 6240, 1440, 1120, 2464, 36960, 84864, 14976, 8064, 9856, 29568, 561792, 1188096, 169728, 69888, 59136, 98560, 374528, 8614144, 16972800, 2036736, 678912, 439296, 506880, 1070080, 4922368, 132903936, 246105600, 25459200, 7128576, 3734016, 3294720, 4815360

Offset

0,2

Comments

Generalization of super Catalan numbers of Gessel, A068555, based on Patalan numbers of order 4, A025749.

Links

Table of n, a(n) for n=0..41.

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)*(16*n-4)/(n+k), a(n,k) = a(n,k-1)*(16*k-12)/(n+k).

G.f.: ((x/(1-16*x)^(3/4)+y/(1-16*y)^(1/4))/(x+y-16*x*y).

Example

a(0..4, 0..4) is:
1      4      40     480    6240
12     24     160    1440   14976
168    224    1120   8064   69888
2464   2464   9856   59136  439296
36960  29568  98560  506880 3294720

Crossrefs

Cf. A068555, A025749, A216702 (first column), A034385 (first row), A248324.

Sequence in context: A149330 A149331 A009532 * A344122 A328533 A265127

Adjacent sequences: A248322 A248323 A248324 * A248326 A248327 A248328

Keyword

nonn,tabl,easy

Author

Tom Richardson, Oct 04 2014

Status

approved