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A069322 Square array read by antidiagonals of floor[(n+k)^(n+k)/(n^n*k^k)]. 1
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, 17, 65, 119, 119, 65, 17, 1, 1, 20, 89, 198, 256, 198, 89, 20, 1, 1, 23, 117, 307, 484, 484, 307, 117, 23, 1, 1, 25, 149, 449, 837, 1024, 837, 449, 149, 25, 1, 1, 28, 184, 629 (list; table; graph; refs; listen; history; text; internal format)
OFFSET

0,5

COMMENTS

T(n,k)*sqrt(3)/(n*k*Pi) provides a rough approximation for A067059.

a(n,k) is an analog of the binomial coefficients over transformations instead of permutations. - Chad Brewbaker, Nov 25 2013

LINKS

G. C. Greubel, Table of n, a(n) for the first 100 rows, flattened

FORMULA

a(n,k) = (n^n) /((k^k)*((n-k)^(n-k))). - Chad Brewbaker, Nov 25 2013

EXAMPLE

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.

MATHEMATICA

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 *)

PROG

(Ruby)

def transitorial(n)

    return n**n

end

def transnomial(n, k)

       return transitorial(n)/(transitorial(k) *transitorial(n-k))

end

0.upto(15) do |i|

   0.upto(i) do |j|

       print transnomial(i, j).to_s + " "

   end

   puts ""

end # Chad Brewbaker, Nov 25 2013

(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

CROSSREFS

Initial columns and rows are A000012 and A060644, main diagonal is A000302.

Sequence in context: A144463 A174376 A131399 * A208332 A075112 A202687

Adjacent sequences:  A069319 A069320 A069321 * A069323 A069324 A069325

KEYWORD

nonn,tabl

AUTHOR

Henry Bottomley, Mar 14 2002

STATUS

approved

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Last modified September 22 10:58 EDT 2020. Contains 337289 sequences. (Running on oeis4.)