|
|
EXAMPLE
| If the successive inverse binomial transforms are placed in a table,
then we see that the diagonal consists of the factorials:
n=0:[(1),2,6,33,232,2045,21636,267043,3766848,59776137,1053986500,...];
n=1:[1,(1),3,20,129,1164,12265,151458,2136337,33901640,597761361,...];
n=2:[1,0,(2),13,64,693,6856,86175,1210896,19228825,339012304,...];
n=3:[1,-1,3,(6),25,482,3429,50908,678465,10937430,192150469,...];
n=4:[1,-2,6,-7,(24),381,844,36291,341728,6433865,107801436,...];
n=5:[1,-3,11,-32,97,(120),-839,37158,55953,4638052,54573025,...];
n=6:[1,-4,18,-75,304,-811,(720),40783,-262608,5542425,6069736,...];
n=7:[1,-5,27,-142,729,-3282,11941,(5040),-497279,9166130,...];
n=8:[1,-6,38,-239,1480,-8643,45844,-178557,(40320),12301705,...];
n=9:[1,-7,51,-372,2689,-18844,125289,-741974,3354513,(362880),...].
|
