login
A330764
Number of series-reduced rooted trees whose leaves are sets with a total of n elements covering an initial interval of positive integers.
3
1, 3, 18, 194, 2944, 57959, 1398858, 39981994, 1320143478, 49439258516, 2070409961552, 95867076538834, 4863079990663528, 268198764863998103, 15977057268090388836, 1022415045656417706598, 69946606996018140613292, 5094427098628436561252367, 393558075509405403487404506
OFFSET
1,2
LINKS
EXAMPLE
The a(3) = 18 trees:
(123) ((1)(12)) ((1)(1)(1))
((1)(23)) ((2)(12)) ((1)((1)(1)))
((2)(13)) ((1)(2)(2))
((3)(12)) ((1)(1)(2))
((1)(2)(3)) ((1)((2)(2)))
((1)((2)(3))) ((1)((1)(2)))
((2)((1)(3))) ((2)((1)(2)))
((3)((1)(2))) ((2)((1)(1)))
PROG
(PARI)
EulerT(v)={Vec(exp(x*Ser(dirmul(v, vector(#v, n, 1/n))))-1, -#v)}
R(n, k)={my(v=[]); for(n=1, n, v=concat(v, EulerT(concat(v, [binomial(k, n)]))[n])); v}
seq(n)={sum(k=1, n, R(n, k)*sum(r=k, n, binomial(r, k)*(-1)^(r-k)))}
CROSSREFS
Row sums of A330763.
Cf. A330469 (leaves are multisets).
Sequence in context: A259336 A308134 A160707 * A367487 A377545 A277355
KEYWORD
nonn
AUTHOR
Andrew Howroyd, Dec 29 2019
STATUS
approved