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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 (list; graph; refs; listen; history; text; internal format)
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*n-9)*5^n+(6*n^2-18*n+3)*3^n-4*n^3+18*n^2-8*n-15)/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[n-1, k] + (n-2k+1) t[n-1, k-1]; a[n_] := t[n, 3]; Table[a[n], {n, 6, 23}] (* Jean-Fran├žois Alcover, Feb 09 2016 *)

PROG

(MAGMA) [(3*7^n-(6*n-9)*5^n+(6*n^2-18*n+3)*3^n-4*n^3+18*n^2-8*n-15)/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

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Last modified December 18 12:06 EST 2018. Contains 318229 sequences. (Running on oeis4.)