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A066045 Triangle T(n,k) defined by Sum_{1<=k<=n} T(n,k)*u^k*t^n/n! = exp(((1-t)*(1-t^2)*(1-t^3)...)^(-u)-1).

%I A066045 #9 Sep 29 2023 18:32:06
%S A066045 1,3,2,8,18,5,42,118,90,15,144,900,1075,450,52,1440,6788,12375,8475,
%T A066045 2340,203,5760,61824,141470,140175,63700,12789,877,75600,586584,
%U A066045 1700580,2218335,1441440,474614,73668,4140,524160,6064416,21677980
%N A066045 Triangle T(n,k) defined by Sum_{1<=k<=n} T(n,k)*u^k*t^n/n! = exp(((1-t)*(1-t^2)*(1-t^3)...)^(-u)-1).
%e A066045 Triangle begins:
%e A066045   [1],
%e A066045   [3, 2],
%e A066045   [8, 18, 5],
%e A066045   [42, 118, 90, 15],
%e A066045   [144, 900, 1075, 450, 52],
%e A066045   ...
%Y A066045 Cf. A058892 (row sums), A000110, A008298, A038048.
%K A066045 nonn,tabl
%O A066045 1,2
%A A066045 _Vladeta Jovovic_, Dec 29 2001