A308677 Kuba-Panholzer Table 2 pattern 312, 213 for Stirling permutation k = 2.

3, 23, 155, 1014, 6580, 42636, 276507, 1796300, 11692395, 76257675, 498286932, 3261636728, 21384163320, 140407901032, 923165093595, 6077239852824, 40052346318985, 264243349910925, 1745013401135235, 11533997779931550, 76298933599198800, 505113085597039920, 3346315941511650900

Offset

3,1

Links

Table of n, a(n) for n=3..25.

Markus Kuba, Alois Panholzer, Stirling permutations containing a single pattern of length three, Australasian Journal of Combinatorics (2019) Vol. 74, No. 2, 216-239.

Formula

For k = 2, a(n) = binomial(n*k - 2k + n - 1, n - 1) - (1 / k(n - 1) + 1) binomial((k + 1)(n - 1)/(n - 1))

Mathematica

With[{k = 2}, Table[Binomial[k n + n - 2 k - 1, n - 1] - (1/(k (n - 1) + 1)) Binomial[(k + 1) (n - 1), n - 1], {n, 3, 25}]]

Crossrefs

Cf. A001700, A003517.

Sequence in context: A197176 A264461 A006184 * A209011 A164536 A037789

Adjacent sequences: A308674 A308675 A308676 * A308678 A308679 A308680

Keyword

nonn,easy

Author

Michael De Vlieger, Jun 16 2019

Status

approved