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%I #13 Aug 30 2019 04:02:11
%S 1,3,1,10,3,1,35,10,9,3,1,126,35,30,10,9,3,1,462,126,105,100,35,30,27,
%T 10,9,3,1,1716,462,378,350,126,105,100,90,35,30,27,10,9,3,1,6435,1716,
%U 1386,1260,1225,462,378,350,315,300,126,105,100,90,81,35,30,27,10,9,3,1
%N A certain partition array in Abramowitz-Stegun order (A-St order), called M_0(3)/M_0.
%C The sequence of row lengths is A000041 (partition numbers) [1, 2, 3, 5, 7, 11, 15, 22, 30, 42, ...].
%C For the A-St order of partitions see the Abramowitz-Stegun reference given in A117506.
%C Partition number array M_0(3)= A134283 with each entry divided by the corresponding one of the partition number array M_0 = M_0(2) = A048996; in short M_0(3)/M_0.
%H M. Abramowitz and I. A. Stegun, eds., <a href="http://www.convertit.com/Go/ConvertIt/Reference/AMS55.ASP">Handbook of Mathematical Functions</a>, National Bureau of Standards, Applied Math. Series 55, Tenth Printing, 1972 [alternative scanned copy].
%H W. Lang, <a href="/A134284/a134284.txt">First 10 rows and more</a>.
%F a(n,k) = Product_{j=1..n} s2(3,j,1)^e(n,k,j) with s2(3,n,1) = A035324(n,1) = A001700(n-1) = binomial(2*n-1,n) and with the exponent e(n,k,j) of j in the k-th partition of n in the A-St ordering of the partitions of n.
%F a(n,k) = A134283(n,k)/A048996(n,k) (division of partition arrays M_0(3) by M_0).
%e [1]; [3,1]; [10,3,1]; [35,10,9,3,1]; [126,35,30,10,9,3,1]; ...
%e a(4,3) = 9 = 3^2 because (2^2) is the k=4 partition of n=4 in A-St order and s2(3,2,1)=3.
%Y Cf. A134826 (row sums coinciding with those of triangle A134285).
%K nonn,easy,tabf
%O 1,2
%A _Wolfdieter Lang_, Nov 13 2007
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