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

1,2

Links

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

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 A277355 A135077

Adjacent sequences: A330761 A330762 A330763 * A330765 A330766 A330767

Keyword

nonn

Author

Andrew Howroyd, Dec 29 2019

Status

approved