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, 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

Links

Table of n, a(n) for n=0..44.

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).

Cf. A350462, A350291.

Sequence in context: A349776 A305622 A269940 * A341339 A084257 A365803

Adjacent sequences: A350460 A350461 A350462 * A350464 A350465 A350466

Keyword

nonn,tabl

Author

Peter Luschny, Mar 12 2022

Status

approved