A347700 Triangle read by rows: For n >= 1, 0 <= k <= n-1, T(n,k) is Sharp's function w_n(k) arising in the calculation of the number of vacuously transitive relations on n points.

2, 3, 4, 4, 6, 14, 5, 8, 47, 32, 6, 10, 120, 192, 60, 7, 12, 266, 912, 583, 100, 8, 14, 524, 3622, 4804, 1474, 154, 9, 16, 954, 12508, 34262, 20168, 3291, 224, 10, 18, 1624, 38590, 213880, 254290, 72228, 6700, 312, 11, 20, 2629, 108352, 1185530, 2906420, 1583622, 229408, 12702, 420, 12, 22, 4074, 281062, 5908844, 29904182, 33170672, 8606718, 662410, 22738, 550, 13, 24, 6097, 681332, 26795318, 277167464, 643126074, 328893052

Offset

1,1

Comments

For the precise definition of T(n,k) see Sharp (1973).

Links

Table of n, a(n) for n=1..74.

H. Sharp, Jr., Enumeration of vacuously transitive relations, Discrete Math. 4 (1973), 185-196.

Example

Triangle begins:
  2;
  3,  4;
  4,  6,  14;
  5,  8,  47,  32;
  6, 10, 120, 192, 60;
...

Crossrefs

Row sums are A003041.

Cf. A347699, A347701.

Sequence in context: A347713 A056880 A053273 * A049988 A079247 A382204

Adjacent sequences: A347697 A347698 A347699 * A347701 A347702 A347703

Keyword

nonn,tabl

Author

N. J. A. Sloane, Oct 13 2021

Extensions

Terms a(16) onward added by Max Alekseyev, Apr 01 2026

Status

approved