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)*(49*n-7)/(n+k), T(n,k) = T(n,k-1)*(49*k-42)/(n+k).
G.f.: (x/(1-49*x)^(6/7)+y/(1-49*y)^(1/7))/(x+y-49*x*y).
T(n,k) = (-1)^k*49^(n+k)*binomial(n-1/7,n+k).
EXAMPLE
T(0..4,0..4) is
1 7 196 6860 264110
42 147 2744 72030 2218524
1911 4459 62426 1310946 33647614
89180 156065 1747928 30588740 672952280
4213755 5899257 55059732 825895980 15898497615
PROG
(PARI) matrix(5, 5, nn, kk, n=nn-1; k=kk-1; (-1)^k*49^(n+k)*binomial(n-1/7, n+k)) \\ Michel Marcus, Oct 09 2014
CROSSREFS
KEYWORD
AUTHOR
Tom Richardson, Oct 04 2014
STATUS
approved