来自在线整数百科全书的问候语!http://oeis.org/ Search: id:a176735 Showing 1-1 of 1 %I A176735 %S A176735 1,9,91,1019,12501,166589,2394751,36920799,607496041,10622799089, %T A176735 196677847971,3843107102339,79025598374461,1705654851091749, %U A176735 38551739502886471,910569176481673319,22431936328103456721,575367515026293191129,15340898308261381733611,424560869593530584247819 %N A176735 a(n) = (n+8)*a(n-1) + (n-1)*a(n-2), a(-1)=0, a(0)=1. %C A176735 a(n) enumerates the possibilities for distributing n beads, n>=1, labeled differently from 1 to n, over a set of (unordered) necklaces, excluding necklaces with exactly one bead, and k=9 indistinguishable, ordered, fixed cords, each allowed to have any number of beads. 无枝项链和无茎索在计数中贡献了因子1,例如A(0):=1×1=1。见A000 0255的描述与一个固定的珠子线。这产生了(n)子阶乘序列{a000 0166(n)}和序列{a049 38(n)=(n+8)的指数(Aka二项)卷积。8!}。见项链和绳索问题在A000 0153评论。因此,输入的递归成立。这个评论源于一个由Malin Sjodahl发现的对于某些夸克和胶子图(2月27日2010)的组合问题的递归项。n,a(n)n=0…400的表%F A17635 E.G.F.(EXP(-x)/(1-x))*(1 /(1-x)^ 9)=EXP(-x)/(1-x)^ 10,相当于给定的递推.% f f A1767 35 A(n)=A0867 64(n+9,9).5月27日,2016岁的E.A17635项链和9条绳索的问题。对于n=4,考虑以下4个弱的2部分组成:(4,0),(3,1),(2,2),和(0,4),其中(1,3)不出现,因为没有带1珠的项链。这些作文分别起作用!4*1,二项式(4,3)*!3 *C9(1),(二项式(4,2)*!2)*C9(2),1*C9(4)与子因子!N:= A000 0166(n)(见项链注释)和C9(n):=A049 38(n)个数,用于纯9线问题(参见关于A000 0153中的K-线问题的E.F.F的注释;这里为K=9:1(/ 1-x)^ 9)。This adds up as 9 + 4*2*9 + (6*1)*90 + 11880 = 12501 = a(4). %t A176735 RecurrenceTable[{a[0]==1,a[1]==9,a[n]==(n+8)a[n-1]+(n-1)a[n-2]},a[n],{n,20}] (* _Harvey P. Dale_, Oct 20 2011 *) %t A176735 Table[(-1)^n HypergeometricPFQ[{10, -n}, {}, 1], {n, 0, 20}] (* _Benedict W. J. Irwin_, May 27 2016 *) %Y A176735 Cf. A176734 (necklaces and k=8 cords). %K A176735 nonn,easy %O A176735 0,2 %A A176735 _Wolfdieter Lang_, Jul 14 2010 # Content is available under The OEIS End-User License Agreement: http://oeis.org/LICENSE