cp's OEIS Frontend

A301761 Number of ways to choose a rooted partition of each part in a constant rooted partition of n.

%I A301761 #9 Aug 27 2018 01:52:21
%S A301761 1,1,2,3,5,6,13,12,26,31,57,43,150,78,224,293,484,232,1190,386,2260,
%T A301761 2087,2558,1003,11154,4701,7889,13597,30041,3719,83248,5605,95006,
%U A301761 84486,63506,251487,654394,17978,169864,490741,2290336,37339,4079503,53175,3979370
%N A301761 Number of ways to choose a rooted partition of each part in a constant rooted partition of n.
%C A301761 A rooted partition of n is an integer partition of n - 1.
%H A301761 Andrew Howroyd, <a href="/A301761/b301761.txt">Table of n, a(n) for n = 1..1000</a>
%F A301761 a(n) = Sum_{d | n-1} A000041((n-1)/d-1)^d for n > 1. - _Andrew Howroyd_, Aug 26 2018
%e A301761 The a(7) = 13 rooted twice-partitions:
%e A301761 (5), (41), (32), (311), (221), (2111), (11111),
%e A301761 (2)(2), (2)(11), (11)(2), (11)(11),
%e A301761 (1)(1)(1),
%e A301761 ()()()()()().
%t A301761 Table[Sum[PartitionsP[n/d-1]^d,{d,Divisors[n]}],{n,50}]
%o A301761 (PARI) a(n)=if(n==1, 1, sumdiv(n-1, d, numbpart((n-1)/d-1)^d)) \\ _Andrew Howroyd_, Aug 26 2018
%Y A301761 Cf. A000005, A000041, A002865, A018818, A063834, A093637, A127524, A260685, A271619, A279787, A301422, A301462, A301467, A301480, A301706.
%K A301761 nonn
%O A301761 1,3
%A A301761 _Gus Wiseman_, Mar 26 2018