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A301751
Number of ways to choose a rooted partition of each part in a strict rooted partition of n.
2
1, 1, 1, 3, 5, 10, 17, 32, 54, 100, 166, 289, 494, 840, 1393, 2400, 3931, 6498, 10861, 17728, 28863, 47557, 77042, 123881, 201172, 322459, 517032, 827993, 1316064, 2084632, 3328204, 5236828, 8247676, 13005652, 20417628, 31934709, 49970815, 77789059, 121144373
OFFSET
1,4
COMMENTS
A rooted partition of n is an integer partition of n - 1.
LINKS
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
KEYWORD
nonn
AUTHOR
Gus Wiseman, Mar 26 2018
STATUS
approved