A290035 Number of set partitions of [n] having exactly six blocks of size > 1.

10395, 405405, 8828820, 142101960, 1889157270, 21997025050, 232434862660, 2281515816580, 21144158620585, 187205367167455, 1597460349645160, 13226705948208060, 106823347196076588, 845052099612035700, 6569883153685651800, 50334986592592563576

Offset: 12

Author

Alois P. Heinz, Jul 18 2017

Keywords

• nonn
• easy

Links

• Alois P. Heinz, Table of n, a(n) for n = 12..1000
• Wikipedia, Partition of a set
• Index entries for linear recurrences with constant coefficients, signature (84, -3360, 85204, -1538460, 21061260, -227279184, 1984514004, -14280788214, 85828895124, -435042172944, 1872967672764, -6883607484444, 21668771179044, -58531231913904, 135734401224444, -270012108240369, 459750737925864, -667610836187984, 822369705703584, -852988627596768, 737567996531840, -524515347742464, 301116476275200, -135928473663744, 46399971446784, -11247176540160, 1723509964800, -125411328000).

Crossrefs

Column k=6 of A124324.

Cf. A290034.

Formula

E.g.f.: (exp(x)-x-1)^6/6!*exp(x).

G.f.: -(46416180096*x^15 -267702314880*x^14 [phone]*x^13 -1174802003648*x^12 [phone]*x^11 -1085757157800*x^10 [phone]*x^9 -313912715655*x^8 [phone]*x^7 -31611210400*x^6 [phone]*x^5 -1067591910*x^4 [phone]*x^3 -9702000*x^2 +467775*x -10395)*x^12 / ((7*x-1) *(6*x-1)^2 *(5*x-1)^3 *(4*x-1)^4 *(3*x-1)^5 *(2*x-1)^6 *(x-1)^7).

a(0) = a(1) = 0, for n>1 a(n) = 7*a(n-1) + (n-1)*A290034(n-2). - Ray Chandler, Jul 21 2017