A350462 - OEIS

%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