OFFSET
1,2
COMMENTS
Number of monotone n-weightings of a certain connected bipartite digraph. A monotone n-(vertex) weighting of a digraph D=(V,E) is a function w: V -> {0,1,..,n-1} such that w(v1)<=w(v2) for every arc (v1,v2) from E.
LINKS
G. C. Greubel, Table of n, a(n) for n = 1..1000
Goran Kilibarda and Vladeta Jovovic, Antichains of Multisets, J. Integer Seqs., Vol. 7, 2004.
Index entries for linear recurrences with constant coefficients, signature (6,-15,20,-15,6,-1).
FORMULA
a(n) = n + 10*binomial(n, 2) + 30*binomial(n, 3) + 35*binomial(n, 4) + 14*binomial(n, 5).
a(n) = n*(n+1)*(2*n+1)*(7*n^2 + 7*n + 6)/120.
G.f.: x*(1+6*x+6*x^2+x^3)/(1-x)^6. - Colin Barker, Apr 01 2012
MATHEMATICA
Table[n*(n+1)*(2*n+1)*(7*n^2 + 7*n + 6)/120, {n, 1, 25}] (* G. C. Greubel, Oct 07 2017 *)
PROG
(PARI) for(n=1, 25, print1(n*(n+1)*(2*n+1)*(7*n^2 + 7*n + 6)/120, ", ")) \\ G. C. Greubel, Oct 07 2017
(Magma) [n*(n+1)*(2*n+1)*(7*n^2 + 7*n + 6)/120: n in [1..25]]; // G. C. Greubel, Oct 07 2017
CROSSREFS
KEYWORD
nonn,easy
AUTHOR
Goran Kilibarda, Vladeta Jovovic, Jul 01 2003
STATUS
approved