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%I #12 May 11 2018 12:04:15
%S 1,0,1,0,1,3,0,1,15,10,0,1,63,140,35,0,1,255,1470,1050,126,0,1,1023,
%T 14080,21945,6930,462,0,1,4095,130130,400400,252252,42042,1716,0,1,
%U 16383,1184820,6861855,7747740,2438436,240240,6435
%N T(n, k) = Sum_{j=0..k} (-1)^j*binomial(2*k, j)*(k - j)^(2*n)/(k!)^2, triangle read by rows, n >= 0 and 0 <= k <= n.
%F T(n, k) = A304330(n, k)/(k!)^2.
%F T(n, k) = A304334(n, k)/k!.
%e Triangle starts:
%e [0] 1;
%e [1] 0, 1;
%e [2] 0, 1, 3;
%e [3] 0, 1, 15, 10;
%e [4] 0, 1, 63, 140, 35;
%e [5] 0, 1, 255, 1470, 1050, 126;
%e [6] 0, 1, 1023, 14080, 21945, 6930, 462;
%e [7] 0, 1, 4095, 130130, 400400, 252252, 42042, 1716;
%e [8] 0, 1, 16383, 1184820, 6861855, 7747740, 2438436, 240240, 6435;
%p A304336 := (n, k) -> add((-1)^j*binomial(2*k,j)*(k-j)^(2*n), j=0..k)/(k!)^2:
%p for n from 0 to 8 do seq(A304336(n, k), k=0..n) od;
%o (PARI) T(n, k) = sum(j=0, k, (-1)^j*binomial(2*k, j)*(k - j)^(2*n))/(k!)^2;
%o tabl(nn) = for (n=0, nn, for (k=0, n, print1(T(n,k), ", ")); print); \\ _Michel Marcus_, May 11 2018
%Y Row sums are A304338, T(n,n) = A088218 and A001700, T(n,n-1) ~ A002803, T(n,2) ~ A024036, T(n,3) ~ bisection of A174395.
%Y Cf. A304330, A304334.
%K nonn,tabl
%O 0,6
%A _Peter Luschny_, May 11 2018
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