cp's OEIS Frontend

A301753 Number of ways to choose a strict rooted partition of each part in a rooted partition of n.

%I A301753 #10 Aug 29 2018 02:52:34
%S A301753 1,1,2,3,6,9,16,25,43,66,108,166,269,408,643,975,1517,2277,3497,5223,
%T A301753 7936,11803,17736,26219,39174,57594,85299,124957,183987,268158,392685,
%U A301753 569987,830282,1200843,1740422,2507823,3620550,5197885,7472229,10694865,15319700
%N A301753 Number of ways to choose a strict rooted partition of each part in a rooted partition of n.
%C A301753 A rooted partition of n is an integer partition of n - 1.
%H A301753 Andrew Howroyd, <a href="/A301753/b301753.txt">Table of n, a(n) for n = 1..500</a>
%F A301753 O.g.f.: x * Product_{n > 0} 1/(1 - A000009(n-1) x^n).
%e A301753 The a(7) = 16 rooted twice-partitions:
%e A301753 (5), (32), (41),
%e A301753 (2)(2), (3)(1), (4)(), (21)(1), (31)(),
%e A301753 (1)(1)(1), (2)(1)(), (3)()(), (21)()(),
%e A301753 (1)(1)()(), (2)()()(),
%e A301753 (1)()()()(),
%e A301753 ()()()()()().
%t A301753 nn=50;
%t A301753 ser=x*Product[1/(1-PartitionsQ[n-1]x^n),{n,nn}];
%t A301753 Table[SeriesCoefficient[ser,{x,0,n}],{n,nn}]
%o A301753 (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
%Y A301753 Cf. A002865, A032305, A063834, A093637, A270995, A281113, A296119, A301422, A301462, A301467, A301480, A301706, A301751.
%K A301753 nonn
%O A301753 1,3
%A A301753 _Gus Wiseman_, Mar 26 2018