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%I #7 Mar 07 2021 17:43:45
%S 1,1,1,1,2,1,1,3,3,1,1,4,8,4,1,1,5,17,17,5,1,1,6,32,54,32,6,1,1,7,57,
%T 145,145,57,7,1,1,8,100,368,512,368,100,8,1,1,9,177,945,1649,1649,945,
%U 177,9,1,1,10,320,2530,5392,6250,5392,2530,320,10,1,1,11,593,7073,18785,23401,23401,18785,7073,593,11,1
%N Triangle T(n, k) = k^(n-k) + (n-k)^k with T(0, 0) = 1, read by rows.
%C This sequence is an approximation of Pascal's triangle with interior Kurtosis.
%C Essentially the same as A055652. - _R. J. Mathar_, Feb 19 2009
%H G. C. Greubel, <a href="/A156354/b156354.txt">Rows n = 0..30 of the triangle, flattened</a>
%F T(n, k) = k^(n-k) + (n-k)^k with T(0, 0) = 1.
%F T(n, k) = T(n, n-k).
%F Sum_{k=0..n} T(n,k) = [n=0] + 2*A026898(n-1). - _G. C. Greubel_, Mar 07 2021
%e Triangle begins as:
%e 1;
%e 1, 1;
%e 1, 2, 1;
%e 1, 3, 3, 1;
%e 1, 4, 8, 4, 1;
%e 1, 5, 17, 17, 5, 1;
%e 1, 6, 32, 54, 32, 6, 1;
%e 1, 7, 57, 145, 145, 57, 7, 1;
%e 1, 8, 100, 368, 512, 368, 100, 8, 1;
%e 1, 9, 177, 945, 1649, 1649, 945, 177, 9, 1;
%e 1, 10, 320, 2530, 5392, 6250, 5392, 2530, 320, 10, 1;
%e 1, 11, 593, 7073, 18785, 23401, 23401, 18785, 7073, 593, 11, 1;
%e The interior Kurtosis, T(n,k) - binomial(n, k), is:
%e 0;
%e 0, 0;
%e 0, 0, 0;
%e 0, 0, 0, 0;
%e 0, 0, 2, 0, 0;
%e 0, 0, 7, 7, 0, 0;
%e 0, 0, 17, 34, 17, 0, 0;
%e 0, 0, 36, 110, 110, 36, 0, 0;
%e 0, 0, 72, 312, 442, 312, 72, 0, 0;
%e 0, 0, 141, 861, 1523, 1523, 861, 141, 0, 0;
%e 0, 0, 275, 2410, 5182, 5998, 5182, 2410, 275, 0, 0;
%e 0, 0, 538, 6908, 18455, 22939, 22939, 18455, 6908, 538, 0, 0;
%t T[n_, k_]:= If[n==0, 1, (k^(n-k) + (n-k)^k)];
%t Table[T[n, k], {n,0,12}, {k,0,n}]//Flatten
%o (Sage) flatten([[1 if k==n else k^(n-k) + (n-k)^k for k in [0..n]] for n in [0..12]]) # _G. C. Greubel_, Mar 07 2021
%o (Magma) [k eq 0 select 1 else k^(n-k) + (n-k)^k: k in [0..n], n in [0..12]]; // _G. C. Greubel_, Mar 07 2021
%Y Cf. A026898.
%K nonn,tabl
%O 0,5
%A _Roger L. Bagula_, Feb 08 2009
%E Edited by _G. C. Greubel_, Mar 07 2021
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