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EXAMPLE
| Note the diagonal {(n+1)*a(n)} in array of iterated binomial transforms of this sequence:
[1, 1, 4, 30, 344, 5470, 113892, 2988426,..]
[1,_2, 7, 46, 493, 7536, 152539, 3913722,..]
[1, 3,_12, 74, 728, 10542, 206188, 5158778,..]
[1, 4, 19,_120, 1109, 15058, 282039, 6851820,..]
[1, 5, 28, 190,_1720, 22014, 391732, 9185754,..]
[1, 6, 39, 290, 2669,_32820, 553867, 12457646,..]
[1, 7, 52, 426, 4088, 49486,_797244, 17128362,..]
[1, 8, 67, 604, 6133, 74742, 1164823,_23907408,..]
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