OFFSET
3,2
REFERENCES
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 = 3..1000
R. M. Baer and P. Brock, Natural sorting over permutation spaces, Math. Comp. 22 1968 385-410.
J. M. Hammersley, A few seedings of research, in Proc. Sixth Berkeley Sympos. Math. Stat. and Prob., ed. L. M. le Cam et al., Univ. Calif. Press, 1972, Vol. I, pp. 345-394.
FORMULA
a(n) ~ 3^(2*n + 4 + 1/2)/(16*Pi*n^4). - Vaclav Kotesovec, Aug 16 2013
MAPLE
a:= proc(n) option remember; `if`(n<3, 0, `if`(n=3, 1,
(18*(n-1)*(2*n-5)*(3*n^2+2*n-3)*(n-2)^2*a(n-3)
-(n-1)*(147*n^5-553*n^4+199*n^3+937*n^2-790*n+96)*a(n-2)
+(n+1)*(42*n^5-146*n^4+21*n^3+171*n^2+14*n-48)*a(n-1))/
((n-3)*(n+1)*(3*n^2-4*n-2)*(n+2)^2)))
end:
seq(a(n), n=3..30); # Alois P. Heinz, Sep 28 2012
MATHEMATICA
h[l_List] := Module[{n = Length[l]}, Total[l]!/Product[Product[1+l[[i]]-j+Sum[If[l[[k]] >= j, 1, 0], {k, i+1, n}], {j, 1, l[[i]]}], {i, 1, n}]]; g[n_, i_, l_List] := If[n == 0 || i == 1, h[Join[l, Array[1&, n]]]^2, If[i<1, 0, Sum[g[n-i*j, i-1, Join[l, Array[i&, j]]], {j, 0, n/i}]]]; T[n_] := Table[g[n-k, Min[n-k, k], {k}], {k, 1, n}]; Table[T[n], {n, 3, 24}][[All, 3]] (* Jean-François Alcover, Mar 11 2014, after Alois P. Heinz *)
CROSSREFS
KEYWORD
nonn
AUTHOR
EXTENSIONS
More terms from Pab Ter (pabrlos2(AT)hotmail.com), Oct 17 2005
STATUS
approved