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A301753
Number of ways to choose a strict rooted partition of each part in a rooted partition of n.
2
1, 1, 2, 3, 6, 9, 16, 25, 43, 66, 108, 166, 269, 408, 643, 975, 1517, 2277, 3497, 5223, 7936, 11803, 17736, 26219, 39174, 57594, 85299, 124957, 183987, 268158, 392685, 569987, 830282, 1200843, 1740422, 2507823, 3620550, 5197885, 7472229, 10694865, 15319700
OFFSET
1,3
COMMENTS
A rooted partition of n is an integer partition of n - 1.
LINKS
FORMULA
O.g.f.: x * Product_{n > 0} 1/(1 - A000009(n-1) x^n).
EXAMPLE
The a(7) = 16 rooted twice-partitions:
(5), (32), (41),
(2)(2), (3)(1), (4)(), (21)(1), (31)(),
(1)(1)(1), (2)(1)(), (3)()(), (21)()(),
(1)(1)()(), (2)()()(),
(1)()()()(),
()()()()()().
MATHEMATICA
nn=50;
ser=x*Product[1/(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(1/prod(k=1, n-1, 1 - u[k]*x^k + O(x^n)))} \\ Andrew Howroyd, Aug 29 2018
KEYWORD
nonn
AUTHOR
Gus Wiseman, Mar 26 2018
STATUS
approved