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
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).
Crossrefs
Column k=5 of A124324.
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).