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 A134133 A certain partition array in Abramowitz-Stegun order (A-St order). 7

%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 Abramowitz-Stegun order (A-St 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 k-th partition of n in the A-St 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

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Last modified May 18 16:07 EDT 2021. Contains 343995 sequences. (Running on oeis4.)