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%I #10 Apr 12 2013 12:36:07
%S 0,1,3,2,12,240,3,27,1080,226800,4,48,2880,1209600,3657830400,5,75,
%T 6000,3780000,22861440000,1267438233600000,6,108,10800,9072000,
%U 82301184000,9125555281920000,11274806061917798400000
%N Triangle T[r,c]=(r-1)*binomial(r-1,c-1)*(c-1)!*A093883(c), read by rows.
%C T[b,d] gives the number of positive numbers that can be written in base b with d(d+1)/2 digits such that for each k=1,...,d some digit appears exactly k times, cf. A218560, A167819, A218556 and related sequences.
%F T[r,1] = r-1. T[r,2] = 3(r-1)^2. T[r,3] = 60(r-2)(r-1)^2, etc.
%e The first 6 rows of the triangle are:
%e r=1: 0;
%e r=2: 1, 3;
%e r=3: 2, 12, 240;
%e r=4: 3, 27, 1080, 226800;
%e r=5: 4, 48, 2880, 1209600, 3657830400;
%e r=6: 5, 75, 6000, 3780000, 22861440000, 1267438233600000.
%e Row 2 counts the numbers 1 and 4=100[2], 5=101[2], 6=110[2].
%e Row 3 counts the numbers {1, 2} and {9=100[3], 10=101[3], 12=110[3], 14=112[3], 16=121[3], ..., 25=221[3]} and {248=100012[3], ..., 714=222110[3]}.
%o (PARI) T(r,c)=(r-1)*binomial(r-1,c-1)*(c-1)!*A093883(c)
%K nonn,tabl
%O 1,3
%A _M. F. Hasler_, Nov 02 2012
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