A301754 - OEIS

%I #9 Aug 29 2018 02:52:43

%S 1,1,1,2,3,5,8,13,18,29,44,67,100,150,217,326,470,690,1011,1463,2099,

%T 3049,4355,6214,8886,12632,17885,25377,35763,50252,70942,99246,138600,

%U 193912,270286,375471,522224,723010,1000435,1383002,1907724,2624492,3613885

%N Number of ways to choose a strict rooted partition of each part in a strict rooted partition of n.

%C A rooted partition of n is an integer partition of n - 1.

%H Andrew Howroyd, <a href="/A301754/b301754.txt">Table of n, a(n) for n = 1..500</a>

%F O.g.f.: x * Product_{n > 0} (1 + A000009(n-1) x^n).

%e The a(8) = 13 rooted twice-partitions:

%e (6), (51), (42), (321),

%e (5)(), (41)(), (32)(), (4)(1), (31)(1), (3)(2), (21)(2),

%e (3)(1)(), (21)(1)().

%t nn=50;

%t ser=x*Product[1+PartitionsQ[n-1]x^n,{n,nn}];

%t Table[SeriesCoefficient[ser,{x,0,n}],{n,nn}]

%o (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

%Y Cf. A002865, A032305, A063834, A093637, A196545, A279785, A296120, A301422, A301462, A301467, A301480, A301706.

%K nonn

%O 1,4

%A _Gus Wiseman_, Mar 26 2018