OFFSET
1,4
COMMENTS
A rooted partition of n is an integer partition of n - 1.
LINKS
Andrew Howroyd, Table of n, a(n) for n = 1..500
FORMULA
O.g.f.: x * Product_{n > 0} (1 + A000009(n-1) x^n).
EXAMPLE
The a(8) = 13 rooted twice-partitions:
(6), (51), (42), (321),
(5)(), (41)(), (32)(), (4)(1), (31)(1), (3)(2), (21)(2),
(3)(1)(), (21)(1)().
MATHEMATICA
nn=50;
ser=x*Product[1+PartitionsQ[n-1]x^n, {n, nn}];
Table[SeriesCoefficient[ser, {x, 0, n}], {n, nn}]
PROG
(PARI) seq(n)={my(u=Vec(prod(k=1, n-1, 1 + x^k + O(x^n)))); Vec(prod(k=1, n-1, 1 + u[k]*x^k + O(x^n)))} \\ Andrew Howroyd, Aug 29 2018
CROSSREFS
KEYWORD
nonn
AUTHOR
Gus Wiseman, Mar 26 2018
STATUS
approved