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A134279 A certain partition array in Abramowitz-Stegun order (A-St order), called M_3(6)/M_3. 3

%I #13 Aug 29 2019 17:44:54

%S 1,6,1,66,6,1,1056,66,36,6,1,22176,1056,396,66,36,6,1,576576,22176,

%T 6336,4356,1056,396,216,66,36,6,1,17873856,576576,133056,69696,22176,

%U 6336,4356,2376,1056,396,216,66,36,6,1,643458816,17873856,3459456,1463616

%N A certain partition array in Abramowitz-Stegun order (A-St order), called M_3(6)/M_3.

%C Partition number array M_3(6) = A134278 with each entry divided by the corresponding one of the partition number array M_3 = M_3(1) = A036040; in short M_3(6)/M_3.

%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.

%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="/A134279/a134279.txt">First 10 rows and more</a>.

%F a(n,k) = Product_{j=1..n} S2(6,j,1)^e(n,k,j) with S2(6,n,1) = A049385(n,1) = A008548(n) = (5*n-4)(!^5) (quintuple- or 5-factorials) 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) = A134278(n,k)/A036040(n,k) (division of partition arrays M_3(6) by M_3).

%e [1]; [6,1]; [66,6,1]; [1056,66,36,6,1]; [22176,1056,396,66,36,6,1]; ...

%Y Row sums give A134281 (also of triangle A134280).

%Y Cf. A134274 (M_3(5)/M_3 partition array).

%K nonn,easy,tabf

%O 1,2

%A _Wolfdieter Lang_, Nov 13 2007

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