A248328 Square array read by antidiagonals downwards: super Patalan numbers of order 6.

1, 6, 30, 126, 90, 990, 3276, 1260, 1980, 33660, 93366, 24570, 20790, 50490, 1161270, 2800980, 560196, 324324, 424116, 1393524, 40412196, 86830380, 14004900, 6162156, 5513508, 9754668, 40412196, 1414426860, 2753763480, 372130200, 132046200, 89791416, 108694872, 242473176, 1212365880

Offset

0,2

Comments

Generalization of super Catalan numbers, A068555, based on Patalan numbers of order 6, A025751.

Links

Table of n, a(n) for n=0..34.

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)*(36*n-6)/(n+k), a(n,k) = a(n,k-1)*(36*k-30)/(n+k).

G.f.: ((x/(1-36*x)^(5/6)+y/(1-36*y)^(1/6))/(x+y-36*x*y).

a(n,k) = (-1)^k*36^(n+k)*binomial(n-1/6,n+k).

Example

a(0..4,0..4) is
1          6         126       3276      93366
30         90        1260      24570     560196
990        1980      20790     324324    6162156
33660      50490     424116    5513508   89791416
1161270    1393524   9754668   108694872 1548901926

Prog

(PARI) matrix(5, 5, nn, kk, n=nn-1; k=kk-1; (-1)^k*36^(n+k)*binomial(n-1/6, n+k)) \\ Michel Marcus, Oct 09 2014

Crossrefs

Cf. A068555, A025751, A004993 (first row), A004994 (first column), A004995 (second row), A004996 (second column), A248324, A248325, A248326, A248329, A248332.

Sequence in context: A369819 A073970 A074009 * A366058 A356835 A344344

Adjacent sequences: A248325 A248326 A248327 * A248329 A248330 A248331

Keyword

nonn,tabl,easy

Author

Tom Richardson, Oct 04 2014

Status

approved