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 + A000041(n-1) x^n).
EXAMPLE
The a(7) = 17 rooted twice-partitions:
(5), (41), (32), (311), (221), (2111), (11111),
(4)(), (31)(), (22)(), (211)(), (1111)(), (3)(1), (21)(1), (111)(1),
(2)(1)(), (11)(1)().
MATHEMATICA
nn=50;
ser=x*Product[1+PartitionsP[n-1]x^n, {n, nn}];
Table[SeriesCoefficient[ser, {x, 0, n}], {n, nn}]
PROG
(PARI) seq(n)={Vec(prod(k=1, n-1, 1 + numbpart(k-1)*x^k + O(x^n)))} \\ Andrew Howroyd, Aug 29 2018
CROSSREFS
KEYWORD
nonn
AUTHOR
Gus Wiseman, Mar 26 2018
STATUS
approved