

A000507


Number of permutations of [n] with exactly 3 increasing runs of length at least 2.
(Formerly M5323 N2314)


3



61, 1385, 19028, 206276, 1949762, 16889786, 137963364, 1081702420, 8236142455, 61386982075, 450403628440, 3266265481144, 23480284103492, 167687984079924, 1191656966048088, 8436830209386360, 59563995267159825, 419628657826253805
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OFFSET

6,1


REFERENCES

F. N. David, M. G. Kendall and D. E. Barton, Symmetric Function and Allied Tables, Cambridge, 1966, p. 260.
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

Table of n, a(n) for n=6..23.


FORMULA

a(n) = (3*7^n(6*n9)*5^n+(6*n^218*n+3)*3^n4*n^3+18*n^28*n15)/192.


MATHEMATICA

t[n_, 0] = 1; t[n_, k_] /; k > n/2 = 0; t[n_, k_] /; k <= n/2 := t[n, k] = (2k+1) t[n1, k] + (n2k+1) t[n1, k1]; a[n_] := t[n, 3]; Table[a[n], {n, 6, 23}] (* JeanFrançois Alcover, Feb 09 2016 *)


PROG

(MAGMA) [(3*7^n(6*n9)*5^n+(6*n^218*n+3)*3^n4*n^3+18*n^28*n15)/192: n in [6..30]]; // Vincenzo Librandi, Feb 09 2016


CROSSREFS

From Johannes W. Meijer, May 24 2009: (Start)
The a(n) sequence equals the fourth left hand column of A008971.
The a(2*n) sequence equals the fourth left hand column of A160486.
(End)
Sequence in context: A154428 A262017 A060061 * A143011 A211213 A229667
Adjacent sequences: A000504 A000505 A000506 * A000508 A000509 A000510


KEYWORD

nonn


AUTHOR

N. J. A. Sloane.


EXTENSIONS

Definition changed for clarity and for consistency with A008971, and formula and additional terms added by Jon E. Schoenfield, Mar 26 2010


STATUS

approved



