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A330764 Number of series-reduced rooted trees whose leaves are sets with a total of n elements covering an initial interval of positive integers.

%I A330764 #9 Jan 09 2020 19:22:52
%S A330764 1,3,18,194,2944,57959,1398858,39981994,1320143478,49439258516,
%T A330764 2070409961552,95867076538834,4863079990663528,268198764863998103,
%U A330764 15977057268090388836,1022415045656417706598,69946606996018140613292,5094427098628436561252367,393558075509405403487404506
%N A330764 Number of series-reduced rooted trees whose leaves are sets with a total of n elements covering an initial interval of positive integers.
%H A330764 Andrew Howroyd, <a href="/A330764/b330764.txt">Table of n, a(n) for n = 1..200</a>
%e A330764 The a(3) = 18 trees:
%e A330764   (123)          ((1)(12))       ((1)(1)(1))
%e A330764   ((1)(23))      ((2)(12))       ((1)((1)(1)))
%e A330764   ((2)(13))      ((1)(2)(2))
%e A330764   ((3)(12))      ((1)(1)(2))
%e A330764   ((1)(2)(3))    ((1)((2)(2)))
%e A330764   ((1)((2)(3)))  ((1)((1)(2)))
%e A330764   ((2)((1)(3)))  ((2)((1)(2)))
%e A330764   ((3)((1)(2)))  ((2)((1)(1)))
%o A330764 (PARI)
%o A330764 EulerT(v)={Vec(exp(x*Ser(dirmul(v, vector(#v, n, 1/n))))-1, -#v)}
%o A330764 R(n, k)={my(v=[]); for(n=1, n, v=concat(v, EulerT(concat(v, [binomial(k, n)]))[n])); v}
%o A330764 seq(n)={sum(k=1, n, R(n, k)*sum(r=k, n, binomial(r, k)*(-1)^(r-k)))}
%Y A330764 Row sums of A330763.
%Y A330764 Cf. A330469 (leaves are multisets).
%K A330764 nonn
%O A330764 1,2
%A A330764 _Andrew Howroyd_, Dec 29 2019