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A130513 Subtriangle of triangle in A051168: remove central column of A051168 and all columns to the right; now read by upwards diagonals.

%I A130513 #16 Jun 27 2015 06:24:26
%S A130513 1,1,0,2,1,0,5,2,1,0,14,7,3,1,0,42,20,9,3,1,0,132,66,30,12,4,1,0,429,
%T A130513 212,99,40,15,4,1,0,1430,715,333,143,55,18,5,1,0,4862,2424,1144,497,
%U A130513 200,70,22,5,1,0,16796,8398,3978,1768,728,273,91,26,6,1,0,58786,29372,13995
%N A130513 Subtriangle of triangle in A051168: remove central column of A051168 and all columns to the right; now read by upwards diagonals.
%D A130513 A. Errera, Analysis situs: Un problème d'énumération, Memoires Acad. Bruxelles (1931), Serie 2, Vol. 11, No. 6, 26pp.
%F A130513 Sum_{k, 1<=k<=n} T(n,k) = A022553(n); Sum_{k, 1<=k<=n}k*T(n,k) = A002996(n).
%F A130513 T(n,k) = 1/(2n-k) Sum( d | gcd(2n-k,n-k) = mu(d) C((2n-k)/d,(n-k)/d) ). - _Wouter Meeussen_, Jul 20 2008
%e A130513 Triangle T(n,k), 1<=k<=n, begins:
%e A130513 1;
%e A130513 1, 0;
%e A130513 2, 1, 0;
%e A130513 5, 2, 1, 0;
%e A130513 14, 7, 3, 1, 0;
%e A130513 42, 20, 9, 3, 1, 0;
%e A130513 132, 66, 30, 12, 4, 1, 0;
%e A130513 429, 212, 99, 40, 15, 4, 1, 0;
%t A130513 Table[1/(2n-k) Plus@@ (MoebiusMu[ # ]Binomial[(2n-k)/#,(n-k)/# ]&/@ Divisors[GCD[2n-k,n-k]]),{n,12},{k,n}] (* _Wouter Meeussen_, Jul 20 2008 *)
%Y A130513 Cf. A000108, A000150, A050181, A050182, A050183, A050184, A050185.
%K A130513 nonn,tabl
%O A130513 1,4
%A A130513 _Philippe Deléham_, Aug 08 2007
%E A130513 Edited by _N. J. A. Sloane_, Oct 08 2007