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

945, 27720, 460845, 5735730, 59629570, 548307760, 4615040430, 36359543220, 272291994975, 1959812841168, 13667751403475, 92931068213270, 618974154722616, 4053694551645816, 26180738256056076, 167146327568961576, 1056894585385219581, 6629318116295993976

Offset

10,1

Links

Alois P. Heinz, Table of n, a(n) for n = 10..1000

Wikipedia, Partition of a set

Index entries for linear recurrences with constant coefficients, signature (56, -1470, 24052, -275135, 2339340, -15343384, 79518296, -330867999, 1116881584, -3077867318, 6944399940, -12825741073, 19327952588, -23608674132, 23125043824, -17872240112, 10637255232, -4697205696, 1447365888, -277447680, 24883200).

Formula

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

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).

Crossrefs

Column k=5 of A124324.

Sequence in context: A127666 A274756 A335053 * A335055 A133818 A334973

Adjacent sequences: A290031 A290032 A290033 * A290035 A290036 A290037

Keyword

nonn,easy

Author

Alois P. Heinz, Jul 18 2017

Status

approved