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A248328
Square array read by antidiagonals downwards: super Patalan numbers of order 6.
3
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
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)*(36*n-6)/(n+k), T(n,k) = T(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).
T(n,k) = (-1)^k*36^(n+k)*binomial(n-1/6,n+k).
EXAMPLE
T(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
KEYWORD
nonn,tabl,easy,changed
AUTHOR
Tom Richardson, Oct 04 2014
STATUS
approved