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Triangle T(n,k) = n!* A036040(n,k) read by rows, 1 <= k <= A000041(n).
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%I #5 Mar 31 2012 13:23:39

%S 1,2,2,6,18,6,24,96,72,144,24,120,600,1200,1200,1800,1200,120,720,

%T 4320,10800,7200,10800,43200,10800,14400,32400,10800,720,5040,35280,

%U 105840,176400,105840,529200

%N Triangle T(n,k) = n!* A036040(n,k) read by rows, 1 <= k <= A000041(n).

%C Row sums are A137341(n).

%e For row n = 4 the calculations are (1 4 3 6 1) times (24 24 24 24 24 ) yielding (24 96 72 144 24)

%e which sums to A137341(4) = 360.

%e Row n has A000041(n) entries:

%e 1;

%e 2,2;

%e 6,18,6;

%e 24,96,72,144,24;

%e 120,600,1200,1200,1800,1200,120;

%e 720,4320,10800,7200,10800,43200,10800,14400,32400,10800,720;

%Y Cf. A000110, A053529, A137341, A036040, A178801.

%K easy,nonn,tabf

%O 1,2

%A _Alford Arnold_, Jun 23 2010