OFFSET
1,5
REFERENCES
F. N. David, M. G. Kendall and D. E. Barton, Symmetric Function and Allied Tables, Cambridge, 1966, p. 261. (Values for n>=16 are incorrect.)
N. J. A. Sloane, A Handbook of Integer Sequences, Academic Press, 1973 (includes this sequence).
N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, Academic Press, 1995 (includes this sequence).
LINKS
Alois P. Heinz, Table of n, a(n) for n = 1..450 (first 100 terms from Max Alekseyev)
Max A. Alekseyev, On the number of permutations with bounded runs length, arXiv preprint arXiv:1205.4581 [math.CO], 2012-2013. - From N. J. A. Sloane, Oct 23 2012
EXAMPLE
a(5)=8 because we have (1235)4, (1245)3, (1345)2, (2345)1, 5(1234), 4(1235), 3(1245) and 2(1345), where the parentheses surround increasing runs of length 4.
MATHEMATICA
b[u_, o_, t_, k_] := b[u, o, t, k] = If[t == k, (u + o)!, If[Max[t, u] + o < k, 0, Sum[b[u + j - 1, o - j, t + 1, k], {j, 1, o}] + Sum[b[u - j, o + j - 1, 1, k], {j, 1, u}]]];
T[n_, k_] := b[0, n, 0, k] - b[0, n, 0, k + 1];
a[n_] := T[n, 4];
Array[a, 30] (* Jean-François Alcover, Jul 19 2018, after Alois P. Heinz *)
CROSSREFS
KEYWORD
nonn
AUTHOR
EXTENSIONS
Better description from Emeric Deutsch, May 08 2004
Terms a(16)-a(18) corrected and further terms added by Max Alekseyev, May 20 2012
STATUS
approved