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A350463
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, 1, 0, 2, 3, 0, 6, 30, 15, 0, 20, 308, 420, 105, 0, 70, 3420, 10080, 6300, 945, 0, 252, 41052, 242220, 291060, 103950, 10395, 0, 924, 523432, 6048042, 12672660, 8198190, 1891890, 135135, 0, 3432, 6965520, 158012400, 552071520, 581981400, 234594360, 37837800, 2027025
OFFSET
0,5
EXAMPLE
[0] 1;
[1] 0, 1;
[2] 0, 2, 3;
[3] 0, 6, 30, 15;
[4] 0, 20, 308, 420, 105;
[5] 0, 70, 3420, 10080, 6300, 945;
[6] 0, 252, 41052, 242220, 291060, 103950, 10395;
[7] 0, 924, 523432, 6048042, 12672660, 8198190, 1891890, 135135;
MATHEMATICA
Z[n_] := Flatten[Table[{0, Binomial[2 j, j]}, {j, 0, 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. A000984 (column 1), A001147 (main diagonal).
Sequence in context: A349776 A305622 A269940 * A341339 A084257 A365803
KEYWORD
nonn,tabl
AUTHOR
Peter Luschny, Mar 12 2022
STATUS
approved