cp's OEIS Frontend

A301754 Number of ways to choose a strict rooted partition of each part in a strict rooted partition of n.

%I A301754 #9 Aug 29 2018 02:52:43
%S A301754 1,1,1,2,3,5,8,13,18,29,44,67,100,150,217,326,470,690,1011,1463,2099,
%T A301754 3049,4355,6214,8886,12632,17885,25377,35763,50252,70942,99246,138600,
%U A301754 193912,270286,375471,522224,723010,1000435,1383002,1907724,2624492,3613885
%N A301754 Number of ways to choose a strict rooted partition of each part in a strict rooted partition of n.
%C A301754 A rooted partition of n is an integer partition of n - 1.
%H A301754 Andrew Howroyd, <a href="/A301754/b301754.txt">Table of n, a(n) for n = 1..500</a>
%F A301754 O.g.f.: x * Product_{n > 0} (1 + A000009(n-1) x^n).
%e A301754 The a(8) = 13 rooted twice-partitions:
%e A301754 (6), (51), (42), (321),
%e A301754 (5)(), (41)(), (32)(), (4)(1), (31)(1), (3)(2), (21)(2),
%e A301754 (3)(1)(), (21)(1)().
%t A301754 nn=50;
%t A301754 ser=x*Product[1+PartitionsQ[n-1]x^n,{n,nn}];
%t A301754 Table[SeriesCoefficient[ser,{x,0,n}],{n,nn}]
%o A301754 (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 A301754 Cf. A002865, A032305, A063834, A093637, A196545, A279785, A296120, A301422, A301462, A301467, A301480, A301706.
%K A301754 nonn
%O A301754 1,4
%A A301754 _Gus Wiseman_, Mar 26 2018