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A181417 Irregular triangle T(n,k) = binomial(n-1,m-1)*m!*A036040(n,k), where m=A036043(n,k). 0

%I #8 Feb 12 2013 15:38:58

%S 1,1,2,1,12,6,1,24,18,108,24,1,40,80,360,540,960,120,1,60,150,100,900,

%T 3600,900,4800,10800,9000,720,1,84,252,420,1890,9450,6300,9450,16800,

%U 100800,50400,63000,189000,90720,5040,1,112,392,784,490,3528,21168,35280,26460,35280,47040,352800,235200,705600,88200,294000,2352000,1764000,846720,3175200,987840,40320,1,144,576,1344,2016,6048,42336

%N Irregular triangle T(n,k) = binomial(n-1,m-1)*m!*A036040(n,k), where m=A036043(n,k).

%C This is a refinement of the triangle A048743.

%C Row n has A000041(n) elements.

%C The sequence can be derived by expanding A007318 and A000142 and using A036040.

%C For example, row four can be derived using

%C (1 3 3 3 1) times (1 2 2 6 24) times (1 4 3 6 1) = (1 24 18 108 24)

%e The table begins:

%e 1

%e 1...2

%e 1..12...6

%e 1..24..18..108..24

%Y Cf. A045531 (row sums), A048743, A007318, A036040.

%K nonn,tabf

%O 1,3

%A _Alford Arnold_, Oct 22 2010

%E Row 6 onwards and definition by _R. J. Mathar_, Feb 12 2013

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Last modified March 28 18:04 EDT 2024. Contains 371254 sequences. (Running on oeis4.)