|
%I #14 Apr 23 2018 00:35:35
%S 1,1,1,1,4,1,1,6,6,1,1,9,16,9,1,1,12,28,28,12,1,1,14,45,64,45,14,1,1,
%T 17,65,119,119,65,17,1,1,20,89,198,256,198,89,20,1,1,23,117,307,484,
%U 484,307,117,23,1,1,25,149,449,837,1024,837,449,149,25,1,1,28,184,629
%N Square array read by antidiagonals of floor[(n+k)^(n+k)/(n^n*k^k)].
%C T(n,k)*sqrt(3)/(n*k*Pi) provides a rough approximation for A067059.
%C a(n,k) is an analog of the binomial coefficients over transformations instead of permutations. - _Chad Brewbaker_, Nov 25 2013
%H G. C. Greubel, <a href="/A069322/b069322.txt">Table of n, a(n) for the first 100 rows, flattened</a>
%F a(n,k) = (n^n) /((k^k)*((n-k)^(n-k))). - _Chad Brewbaker_, Nov 25 2013
%e Rows start: 1,1,1,1,1,1,...; 1,4,6,9,12,14,...; 1,6,16,28,45,65,...; 1,9,28,64,119,198,...; etc. T(3,5)=floor[8^8/(3^3*5^5)]=floor[16777216 /84375]=floor[198.84...]=198.
%t t[n_, 0] := 1; t[n_, n_] := 1; t[n_, k_] := Floor[(n^n)/((k^k)*((n - k)^(n - k)))]; Table[t[n, k], {n, 0, 20}, {k, 0, n}] // Flatten (* _G. C. Greubel_, Apr 22 2018 *)
%o (Ruby)
%o def transitorial(n)
%o return n**n
%o end
%o def transnomial(n,k)
%o return transitorial(n)/(transitorial(k) *transitorial(n-k))
%o end
%o 0.upto(15) do |i|
%o 0.upto(i) do |j|
%o print transnomial(i,j).to_s + " "
%o end
%o puts ""
%o end # _Chad Brewbaker_, Nov 25 2013
%o (PARI) for(n=0,15, for(k=0,n, print1(if(k==0, 1, if(k==n,1,floor((n^n)/(( k^k)*((n - k)^(n - k)))))), ", "))) \\ _G. C. Greubel_, Apr 22 2018
%Y Initial columns and rows are A000012 and A060644, main diagonal is A000302.
%K nonn,tabl
%O 0,5
%A _Henry Bottomley_, Mar 14 2002
|
