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A301754
Number of ways to choose a strict rooted partition of each part in a strict rooted partition of n.
2
1, 1, 1, 2, 3, 5, 8, 13, 18, 29, 44, 67, 100, 150, 217, 326, 470, 690, 1011, 1463, 2099, 3049, 4355, 6214, 8886, 12632, 17885, 25377, 35763, 50252, 70942, 99246, 138600, 193912, 270286, 375471, 522224, 723010, 1000435, 1383002, 1907724, 2624492, 3613885
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 + 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
KEYWORD
nonn
AUTHOR
Gus Wiseman, Mar 26 2018
STATUS
approved