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Square table, read by antidiagonals, where row e.g.f.s, R(n,x), satisfy: d/dx log( R(n,x) ) = R(n+1,x)^(n+1) with R(n,0) = 1; that is, the logarithmic derivative of the e.g.f. of row n equals the e.g.f. of row n+1 to the n+1 power, for n>=0.
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1, 1, 1, 1, 1, 2, 1, 1, 3, 7, 1, 1, 4, 17, 39, 1, 1, 5, 31, 151, 322, 1, 1, 6, 49, 373, 1901, 3723, 1, 1, 7, 71, 741, 6250, 31851, 57577, 1, 1, 8, 97, 1291, 15457, 136711, 680265, 1147188, 1, 1, 9, 127, 2059, 32186, 416661, 3740137, 17947631, 28557909, 1, 1, 10, 161, 3081, 59677, 1030491, 13908049, 124143598, 571101141, 866222535
1, 3, 21, 243, 4029, 88491, 2450085, 82648611, 3313381293, 154912893243, 8322387603093, 507658268093811, 34817646211022301, 2662987196578490187, 225556061819586894597, 21030571231219899162435
1, 1, 2, 7, 39, 322, 3723, 57577, 1147188, 28557909, 866222535, 31362744620, 1332663774173, 65529062871157, 3684878011841690, 234605021214637355, 16766728751635089083, 1335146927494755758530, 117695398260381996143695
1, 1, 4, 31, 373, 6250, 136711, 3740137, 124143598, 4887140221, 224203589593, 11819532185476, 707883494843341, 47708648339054629, 3589347850731252292, 299381557667730507907, 27518788652896695773041
1, 1, 6, 71, 1291, 32186, 1030491, 40606281, 1911466016, 105145651821, 6645220590851, 476096681256716, 38249611004598701, 3415114289928480181, 336324126216378275806, 36299781235381103548731
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