A350462 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)].

1, 0, 2, 0, 6, 12, 0, 20, 180, 120, 0, 70, 2380, 5040, 1680, 0, 252, 31500, 163800, 151200, 30240, 0, 924, 425964, 4989600, 9702000, 4989600, 665280, 0, 3432, 5885880, 150174024, 554954400, 554954400, 181621440, 17297280

Offset

0,3

Links

Table of n, a(n) for n=0..35.

Example

[0] 1;
[1] 0,    2;
[2] 0,    6,      12;
[3] 0,   20,     180,       120;
[4] 0,   70,    2380,      5040,      1680;
[5] 0,  252,   31500,    163800,    151200,     30240;
[6] 0,  924,  425964,   4989600,   9702000,   4989600,    665280;
[7] 0, 3432, 5885880, 150174024, 554954400, 554954400, 181621440, 17297280;

Mathematica

Z[n_] := Flatten[Table[{0, Binomial[2 j, j]}, {j, 1, n}]];
T[n_, k_] := BellY[2 n, k, Z[2 n - k]];
Table[T[n, k], {n, 0, 6}, {k, 0, n}] // TableForm

Crossrefs

Cf. A350291 (row sums), A000984 (column 1), A001813 (main diagonal).

Cf. A350463.

Sequence in context: A078048 A362186 A335061 * A357367 A110667 A347929

Adjacent sequences: A350459 A350460 A350461 * A350463 A350464 A350465

Keyword

nonn,tabl

Author

Peter Luschny, Mar 12 2022

Status

approved