来自在线整数百科全书的问候语!http://oeis.org/ Search: id:a038675 Showing 1-1 of 1 %I A038675 %S A038675 1,1,3,1,16,10,1,55,165,35,1,156,1386,1456,126,1,399,8456,25368,11970, %T A038675 462,1,960,42876,289920,393030,95040,1716,1,2223,193185,2577135, %U A038675 7731405,5525091,741741,6435,1,5020,803440,19411480,111675850,176644468 %N A038675 Triangle read by rows: T(n,k)=A(n,k)*binomial(n+k-1,n), where A(n,k) are the Eulerian numbers (A008292). %C A038675 Andrews, Theory of Partitions, (1976), discussion of multisets. %C A038675 Let a = a_1,a_2,...,a_n be a sequence on the alphabet {1,2,...,n}. 从左到右扫描A,并通过注意元素的位置来创建一个n置换,从元素到最小值到最大值。参见示例。T(n,k)是对应于具有完全N-K下降的这种排列的序列数。〔5月19日Geffry CrutZez,2010〕0%A038 675 R. L. Graham,D. E. Knuth和O. Patashnik,具体数学,第二版,Addison Wesley,Read,Maul.,1994,P 269(Worpitzky的身份).*%D A038 675 Miklos Bona,排列组合,Chapman和Hall,2004,第6页。[From _Geoffrey Critzer_, May 19 2010] %e A038675 1; %e A038675 1,3; %e A038675 1,16,10; %e A038675 1,55,165,35; %e A038675 1,156,1386,1456,126; %e A038675 ... %e A038675 If a = 3,1,1,2,4,3 the corresponding 6-permutation is 2,3,4,1,6,5 because the first 1 is in the 2nd position, the second 1 is in the 3rd position,the 2 is in the 4th position, the first 3 is in the first position, the next 3 is in the 6th position and the 4 is in the 5th position of the sequence a. [From _Geoffrey Critzer_, May 19 2010] %p A038675 A:=(n,k)->sum((-1)^j*(k-j)^n*binomial(n+1,j),j=0..k): T:=(n,k)->A(n,k)*binomial(n+k-1,n): seq(seq(T(n,k),k=1..n),n=1..10); %t A038675 Table[Table[Eulerian[n, k] Binomial[n + k, n], {k, 0, n - 1}], {n, 1,10}] (* _Geoffrey Critzer_, Jun 13 2013 *) %Y A038675 Cf. A001700, A014449, A000312. %Y A038675 Row sums yield A000312 (Worpitzky's identity). %Y A038675 Cf. A008292. %K A038675 nonn,tabl %O A038675 1,3 %A A038675 _Alford Arnold_ %E A038675 More terms from _Emeric Deutsch_, 在OEIS最终用户许可协议下,可以获得08 2004×2004的内容:HTTP:/OEIS.Org/许可证