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%I #3 Oct 12 2012 14:40:24
%S 1,10,60,282,1149,4272,14932,49996,162369,515886,1613316,4987542,
%T 15290461,46592452,141350412,427459320,1289718225,3884883570,
%U 11688205420,35135919730,105558754461,316995030840,951656181540
%N Third column of triangle A112500.
%C For a combinatorial formula see A112500, case k=3.
%F G.f.: 1/product((1-j*x)^(4-j), j=1..3) = 1/(((1-x)^3)*((1-2*x)^2)*(1-3*x)).
%F a(n) = - 81/8 - (11/4)*(n+1) - (1/2)*binomial(n+2, 2) - 16*(n+1)*2^n + (243/8)*3^n, n>=0 (from partial fractions for g.f.).
%Y Cf. A000295 (second column).
%K nonn,easy
%O 0,2
%A _Wolfdieter Lang_, Oct 14 2005
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