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

1, 3, 18, 194, 2944, 57959, 1398858, 39981994, 1320143478, 49439258516, 2070409961552, 95867076538834, 4863079990663528, 268198764863998103, 15977057268090388836, 1022415045656417706598, 69946606996018140613292, 5094427098628436561252367, 393558075509405403487404506

Offset: 1

Author

Andrew Howroyd, Dec 29 2019

Keywords

• nonn

Examples

			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)))
		

Links

• Andrew Howroyd, Table of n, a(n) for n = 1..200

Crossrefs

Row sums of A330763.

Cf. A330469 (leaves are multisets).

Programs

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)))}