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
a(0,0)=1, a(n,k) = a(n-1,k)*(25*n-5)/(n+k), a(n,k) = a(n,k-1)*(25*k-20)/(n+k).
G.f.: ((x/(1-25*x)^(4/5)+y/(1-25*y)^(1/5))/(x+y-25*x*y).
a(n,k) = (-1)^k*25^(n+k)*binomial(n-1/5,n+k).
EXAMPLE
a(0..4,0..4) is
1 5 75 1375 27500
20 50 500 6875 110000
450 750 5625 61875 825000
10500 13125 78750 721875 8250000
249375 249375 1246875 9796875 97968750
PROG
(PARI) matrix(5, 5, nn, kk, n=nn-1; k=kk-1; (-1)^k*25^(n+k)*binomial(n-1/5, n+k)) \\ Michel Marcus, Oct 09 2014
CROSSREFS
KEYWORD
AUTHOR
Tom Richardson, Oct 04 2014
STATUS
approved