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EXAMPLE
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If the successive inverse binomial transforms are placed in a table,
then we see that the diagonal consists of terms (n+1)^(n-1):
n=0:[(1),2,7,52,541,7446,127939,2641192,63746169,1762380010,...];
n=1:[1,(1),4,36,368,5200,90432,1884736,45817088,1273874688,...];
n=2:[1, 0,(3),26,245,3684,64087,1349214,33003945,922386824,...];
n=3:[1,-1, 4,(16),160,2688,45184,970240,23814144,668975104,...];
n=4:[1,-2,7, 0,(125),2002,31203,705268,17177273,486100710,...];
n=5:[1,-3,12,-28, 176,(1296),21184,524352,12305664,354510080,...];
n=6:[1,-4,19,-74,373, 0,(16807),395866,8645673,260994628,...];
n=7:[1,-5,28,-144,800,-2816, 24192,(262144),5980160,195969024,...];
n=8:[1,-6,39,-244,1565,-8562,56419, 0,(4782969),149083874,...];
n=9:[1,-7,52,-380,2800,-19248,136768,-638912, 6966528,(100000000),..];
n=10:[1,-8,67,-558,4661,-37604,302679,-2112938,17204009, 0,...].
Notice the occurrence of zeros in the secondary diagonal = A138734.
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