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%I #9 Mar 13 2022 07:30:59
%S 1,0,2,0,6,12,0,20,180,120,0,70,2380,5040,1680,0,252,31500,163800,
%T 151200,30240,0,924,425964,4989600,9702000,4989600,665280,0,3432,
%U 5885880,150174024,554954400,554954400,181621440,17297280
%N Table read by rows, T(n, k) = Y(2*n, k, Z(2*n - k)) where Y are the partial Bell polynomials and Z(m) is the list [A126869(j), j = 1..2*(m+1)].
%e [0] 1;
%e [1] 0, 2;
%e [2] 0, 6, 12;
%e [3] 0, 20, 180, 120;
%e [4] 0, 70, 2380, 5040, 1680;
%e [5] 0, 252, 31500, 163800, 151200, 30240;
%e [6] 0, 924, 425964, 4989600, 9702000, 4989600, 665280;
%e [7] 0, 3432, 5885880, 150174024, 554954400, 554954400, 181621440, 17297280;
%t Z[n_] := Flatten[Table[{0, Binomial[2 j, j]}, {j, 1, n}]];
%t T[n_, k_] := BellY[2 n, k, Z[2 n - k]];
%t Table[T[n, k], {n, 0, 6}, {k, 0, n}] // TableForm
%Y Cf. A350291 (row sums), A000984 (column 1), A001813 (main diagonal).
%Y Cf. A350463.
%K nonn,tabl
%O 0,3
%A _Peter Luschny_, Mar 12 2022
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