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%I #6 Nov 08 2017 10:59:57
%S 1,2,1,6,4,3,23,17,13,10,104,81,64,51,41,537,433,352,288,237,196,3100,
%T 2563,2130,1778,1490,1253,1057,19693,16593,14030,11900,10122,8632,
%U 7379,6322,136064,116371,99778,85748,73848,63726,55094,47715,41393
%N Euler-Seidel matrix T(k,n) with start sequence A000248, read by antidiagonals.
%C In an Euler-Seidel matrix, the rows are consecutive pairwise sums and the columns consecutive differences, with the first column the inverse binomial transform of the start sequence.
%H D. Dumont, <a href="http://www.mat.univie.ac.at/~slc/opapers/s05dumont.html">Matrices d'Euler-Seidel</a>, Sem. Loth. Comb. B05c (1981) 59-78.
%F Recurrence: T(0, n) = A000248(n), T(k, n) = T(k-1, n) + T(k-1, n+1).
%e 1,1,3,10,41,196,1057,
%e 2,4,13,51,237,1253,7379,
%e 6,17,64,288,1490,8632,55094,
%e 23,81,352,1778,10122,63726,437810,
%e 104,433,2130,11900,73848,501536,3687056,
%t a248[0] = 1; a248[n_] := Sum[Binomial[n, k]*(n - k)^k, {k, 0, n}];
%t T[0, n_] := T[0, n] = a248[n];
%t T[k_, n_] := T[k, n] = T[k - 1, n] + T[k - 1, n + 1];
%t Table[T[k - n, n], {k, 0, 9}, {n, 0, k}] // Flatten (* _Jean-François Alcover_, Nov 08 2017 *)
%Y First column is A080108, main diagonal is in A098698.
%K nonn,tabl
%O 0,2
%A _Ralf Stephan_, Sep 23 2004
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