OFFSET
0,2
COMMENTS
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
KEYWORD
AUTHOR
Tom Richardson, Oct 04 2014
STATUS
approved