W. Lang, Sep 19 2008

 a(n,m) tabl head (triangle) for A144351 = S1hat(1)


   n\m          1        2       3      4      5     6    7    8    9   10 ...

    1           1        0       0      0      0     0    0    0    0    0

    2           1        1       0      0      0     0    0    0    0    0

    3           2        1       1      0      0     0    0    0    0    0

    4           6        3       1      1      0     0    0    0    0    0

    5          24        8       3      1      1     0    0    0    0    0

    6         120       34       9      3      1     1    0    0    0    0

    7         720      156      36      9      3     1    1    0    0    0

    8        5040      924     166     37      9     3    1    1    0    0

    9       40320     6144     968    168     37     9    3    1    1    0

   10      362880    48096    6372    978    169    37    9    3    1    1
    .
    .
    .
    

The row sums give A107107: [1,1,2,4,11,37,168,926,6181,47651,...].

The first thre rows are A000142(n-1) = (n-1)!, A144352, A144353.


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