%I
%S 1,2,1,6,2,1,24,6,4,2,1,120,24,12,6,4,2,1,720,120,48,36,24,12,8,6,4,2,
%T 1,5040,720,240,144,120,48,36,24,24,12,8,6,4,2,1,40320,5040,1440,720,
%U 576,720,240,144,96,72,120,48,36,24,16,24,12,8,6,4,2,1,362880,40320,10080
%N A certain partition array in AbramowitzStegun order (ASt order).
%C The sequence of row lengths is A000041 (partition numbers) [1, 2, 3, 5, 7, 11, 15, 22, 30, 42,...].
%C Partition number array M_3(2)= A130561 divided by partition number array M_3 = M_3(1) = A036040.
%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 Wolfdieter Lang, <a href="/A134133/a134133.pdf">First 10 rows and more.</a>
%F a(n,k) = A130561(n,k)/A036040(n,k) (division of partition arrays M_3(2) by M_3).
%F a(n,k) = product(j!^e(n,k,j),j=1..n) with the exponent e(n,k,j) of j in the kth partition of n in the ASt ordering of the partitions of n.
%e [1], [2,1], [6,2,1], [24,6,4,2,1], [120,24,12,6,4,2,1], ...
%Y With another ordering of the partitions this becomes A069123.
%Y Cf. A134134 (triangle obtained by summing same m numbers).
%K nonn,easy,tabf
%O 1,2
%A _Wolfdieter Lang_, Oct 12 2007
