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A131237 Number of n X (n+1) matrices with nonnegative integer entries and every row and column sum <= 2.

%I A131237 #8 Aug 26 2015 00:34:44
%S A131237 1,6,79,1837,66021,3374176,231848191,20570267229,2285620096717,
%T A131237 310524073877026,50598503336716611,9732804817777566361,
%U A131237 2180831456691952213969,562835395375423511668692,165687992856606963112408291,55166524646338775672718351481,20620925283916296038124156761241
%N A131237 Number of n X (n+1) matrices with nonnegative integer entries and every row and column sum <= 2.
%D A131237 R. P. Stanley, Enumerative Combinatorics, Cambridge, Vol. 2, 1999; see Problem 5.65(a).
%p A131237 A131237 := proc(n)
%p A131237         exp((x*y*(3-x*y)/2+(x+y)*(2-x*y)/2)/(1-x*y))/sqrt(1-x*y) ;
%p A131237         coeftayl(%,y=0,n+1) ;
%p A131237         coeftayl(%,x=0,n) ;
%p A131237         %*(n+1)!*n! ;
%p A131237         simplify(%) ;
%p A131237 end proc: # _R. J. Mathar_, Sep 30 2011
%Y A131237 Cf. A049088, A131235, A131236.
%K A131237 easy,nonn
%O A131237 0,2
%A A131237 _Vladeta Jovovic_, Jun 20 2007