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A290034 Number of set partitions of [n] having exactly five blocks of size > 1. 3

%I

%S 945,27720,460845,5735730,59629570,548307760,4615040430,36359543220,

%T 272291994975,1959812841168,13667751403475,92931068213270,

%U 618974154722616,4053694551645816,26180738256056076,167146327568961576,1056894585385219581,6629318116295993976

%N Number of set partitions of [n] having exactly five blocks of size > 1.

%H Alois P. Heinz, <a href="/A290034/b290034.txt">Table of n, a(n) for n = 10..1000</a>

%H Wikipedia, <a href="https://en.wikipedia.org/wiki/Partition_of_a_set">Partition of a set</a>

%H <a href="/index/Rec#order_21">Index entries for linear recurrences with constant coefficients</a>, signature (56, -1470, 24052, -275135, 2339340, -15343384, 79518296, -330867999, 1116881584, -3077867318, 6944399940, -12825741073, 19327952588, -23608674132, 23125043824, -17872240112, 10637255232, -4697205696, 1447365888, -277447680, 24883200).

%F E.g.f.: (exp(x)-x-1)^5/5!*exp(x).

%F G.f.: -(9268512*x^10 -38876992*x^9 +72780400*x^8 -79985290*x^7 +57077965*x^6 -27603100*x^5 +9151975*x^4 -2052330*x^3 +297675*x^2 -25200*x +945)*x^10 / ((6*x-1) *(5*x-1)^2 *(4*x-1)^3 *(3*x-1)^4 *(2*x-1)^5 *(x-1)^6).

%Y Column k=5 of A124324.

%K nonn,easy

%O 10,1

%A _Alois P. Heinz_, Jul 18 2017

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Last modified October 16 06:13 EDT 2021. Contains 348040 sequences. (Running on oeis4.)