cp's OEIS Frontend

A301751 Number of ways to choose a rooted partition of each part in a strict rooted partition of n.

%I A301751 #9 Aug 29 2018 02:48:18
%S A301751 1,1,1,3,5,10,17,32,54,100,166,289,494,840,1393,2400,3931,6498,10861,
%T A301751 17728,28863,47557,77042,123881,201172,322459,517032,827993,1316064,
%U A301751 2084632,3328204,5236828,8247676,13005652,20417628,31934709,49970815,77789059,121144373
%N A301751 Number of ways to choose a rooted partition of each part in a strict rooted partition of n.
%C A301751 A rooted partition of n is an integer partition of n - 1.
%H A301751 Andrew Howroyd, <a href="/A301751/b301751.txt">Table of n, a(n) for n = 1..500</a>
%F A301751 O.g.f.: x * Product_{n > 0} (1 + A000041(n-1) x^n).
%e A301751 The a(7) = 17 rooted twice-partitions:
%e A301751 (5), (41), (32), (311), (221), (2111), (11111),
%e A301751 (4)(), (31)(), (22)(), (211)(), (1111)(), (3)(1), (21)(1), (111)(1),
%e A301751 (2)(1)(), (11)(1)().
%t A301751 nn=50;
%t A301751 ser=x*Product[1+PartitionsP[n-1]x^n,{n,nn}];
%t A301751 Table[SeriesCoefficient[ser,{x,0,n}],{n,nn}]
%o A301751 (PARI) seq(n)={Vec(prod(k=1, n-1, 1 + numbpart(k-1)*x^k + O(x^n)))} \\ _Andrew Howroyd_, Aug 29 2018
%Y A301751 Cf. A002865, A032305, A063834, A093637, A271619, A281113, A296118, A300383, A301422, A301462, A301467, A301480, A301706.
%K A301751 nonn
%O A301751 1,4
%A A301751 _Gus Wiseman_, Mar 26 2018