|
%I #13 Jul 21 2017 16:46:48
%S 10395,405405,8828820,142101960,1889157270,21997025050,232434862660,
%T 2281515816580,21144158620585,187205367167455,1597460349645160,
%U 13226705948208060,106823347196076588,845052099612035700,6569883153685651800,50334986592592563576
%N Number of set partitions of [n] having exactly six blocks of size > 1.
%H Alois P. Heinz, <a href="/A290035/b290035.txt">Table of n, a(n) for n = 12..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_28">Index entries for linear recurrences with constant coefficients</a>, 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).
%F E.g.f.: (exp(x)-x-1)^6/6!*exp(x).
%F G.f.: -(46416180096*x^15 -267702314880*x^14 +715470788032*x^13 -1174802003648*x^12 +1324630789300*x^11 -1085757157800*x^10 +667971384675*x^9 -313912715655*x^8 +113562125600*x^7 -31611210400*x^6 +6712800710*x^5 -1067591910*x^4 +123053700*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).
%F a(0) = a(1) = 0, for n>1 a(n) = 7*a(n-1) + (n-1)*A290034(n-2). - _Ray Chandler_, Jul 21 2017
%Y Column k=6 of A124324.
%Y Cf. A290034.
%K nonn,easy
%O 12,1
%A _Alois P. Heinz_, Jul 18 2017
|
