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A267480 Number T(n,k) of words on {1,1,2,2,...,n,n} with longest increasing subsequence of length k; triangle T(n,k), n>=0, 0<=k<=n, read by rows. 5
1, 0, 1, 0, 1, 5, 0, 1, 42, 47, 0, 1, 351, 1527, 641, 0, 1, 3113, 43910, 54987, 11389, 0, 1, 29003, 1302660, 3844840, 2059147, 248749, 0, 1, 280220, 40970298, 265777225, 285588543, 82025038, 6439075, 0, 1, 2782475, 1364750889, 19104601915, 37783672691, 19773928713, 3507289363, 192621953 (list; table; graph; refs; listen; history; text; internal format)
OFFSET

0,6

LINKS

Alois P. Heinz, Rows n = 0..18, flattened

Ferenc Balogh, A generalization of Gessel's generating function to enumerate words with double or triple occurrences in each letter and without increasing subsequences of a given length, arXiv:1505.01389, 2015

Shalosh B. Ekhad and Doron Zeilberger, The Generating Functions Enumerating 12..d-Avoiding Words with r occurrences of each of 1,2, ..., n are D-finite for all d and all r, 2014

FORMULA

T(n,0) = A267479(n,0), T(n,k) = A267479(n,k) - A267479(n,k-1) for k>0.

Sum_{k=0..n-1} T(n,k) = A267532(n).

EXAMPLE

Triangle T(n,k) begins:

  1;

  0, 1;

  0, 1,      5;

  0, 1,     42,       47;

  0, 1,    351,     1527,       641;

  0, 1,   3113,    43910,     54987,     11389;

  0, 1,  29003,  1302660,   3844840,   2059147,   248749;

  0, 1, 280220, 40970298, 265777225, 285588543, 82025038, 6439075;

CROSSREFS

Main diagonal gives A006902.

Row sums give A000680.

Cf. A267479, A267532.

Sequence in context: A216718 A184180 A256069 * A099221 A200415 A200418

Adjacent sequences:  A267477 A267478 A267479 * A267481 A267482 A267483

KEYWORD

nonn,tabl

AUTHOR

Alois P. Heinz, Jan 15 2016

STATUS

approved

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Last modified November 20 18:53 EST 2018. Contains 317413 sequences. (Running on oeis4.)