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).
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-François 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)
KEYWORD
nonn
AUTHOR
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