A218566 Triangle T[r,c]=(r-1)*binomial(r-1,c-1)*(c-1)!*A093883(c), read by rows.
0, 1, 3, 2, 12, 240, 3, 27, 1080, 226800, 4, 48, 2880, 1209600, 3657830400, 5, 75, 6000, 3780000, 22861440000, 1267438233600000, 6, 108, 10800, 9072000, 82301184000, 9125555281920000, 11274806061917798400000
Offset: 1
Examples
The first 6 rows of the triangle are:
r=1: 0;
r=2: 1, 3;
r=3: 2, 12, 240;
r=4: 3, 27, 1080, 226800;
r=5: 4, 48, 2880, 1209600, 3657830400;
r=6: 5, 75, 6000, 3780000, 22861440000, 1267438233600000.
Row 2 counts the numbers 1 and 4=100[2], 5=101[2], 6=110[2].
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]}.
Programs
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PARI
T(r,c)=(r-1)*binomial(r-1,c-1)*(c-1)!*A093883(c)
Formula
T[r,1] = r-1. T[r,2] = 3(r-1)^2. T[r,3] = 60(r-2)(r-1)^2, etc.
Comments