This site is supported by donations to The OEIS Foundation.

 Annual appeal: Please make a donation to keep the OEIS running! Over 6000 articles have referenced us, often saying "we discovered this result with the help of the OEIS". Other ways to donate

 Hints (Greetings from The On-Line Encyclopedia of Integer Sequences!)
 A138771 Triangle read by rows: T(n,k) is the number of permutations of {1,2,...,n} whose 2nd cycle has k entries; each cycle is written with the smallest element first and cycles are arranged in increasing order of their first elements (n>=1; 0<=k<=n-1). For example, 1432=(1)(24)(3) has 2 entries in the 2nd cycle; 3421=(1324) has 0 entries in the 2nd cycle. 3
 1, 1, 1, 2, 3, 1, 6, 11, 5, 2, 24, 50, 26, 14, 6, 120, 274, 154, 94, 54, 24, 720, 1764, 1044, 684, 444, 264, 120, 5040, 13068, 8028, 5508, 3828, 2568, 1560, 720, 40320, 109584, 69264, 49104, 35664, 25584, 17520, 10800, 5040 (list; table; graph; refs; listen; history; text; internal format)
 OFFSET 1,4 COMMENTS T(n,0)=(n-1)!=A000142(n-1). T(n,1)=A000254(n-1). T(n,2)=A001705(n-2). T(n,3)=2*A001711(n-4). T(n,4)=6*A001716(n-5). T(n,n-1)=(n-2)! (n>=2). Sum(kT(n,k),k=0..n-1)=(n-1)!(n-1)(n+2)/4=A138772(n). LINKS FORMULA T(n,k)=(n-1)T(n-1,k)+(n-2)! (1<=k<=n-1). The row generating polynomials P[n](t) satisfy: P[n+1](t)=nP[n](t)+(n-1)!(t+t^2+...+t^n). EXAMPLE T(4,2)=5 because we have (1)(23)(4), (1)(24)(3), (13)(24), (12)(34) and (14)(23). Triangle starts; 1; 1,1; 2,3,1; 6,11,5,2; 24,50,26,14,6; 120,274,154,94,54,24; MAPLE T:=proc (n, k) if k = 0 then factorial(n-1) elif n <= k then 0 else (n-1)*T(n-1, k)+factorial(n-2) end if end proc: for n to 9 do seq(T(n, k), k=0..n-1) end do; CROSSREFS Cf. A000142, A000254, A001705, A001711, A001716, A138772. From Johannes W. Meijer, Oct 16 2009: (Start) A000142 equals for n=>1 the row sums. a(n) = A165680(n) * A165675(n-1). (End) Sequence in context: A155856 A086960 A165675 * A121748 A174893 A008275 Adjacent sequences:  A138768 A138769 A138770 * A138772 A138773 A138774 KEYWORD nonn,tabl AUTHOR Emeric Deutsch, Apr 10 2008 STATUS approved

Lookup | Welcome | Wiki | Register | Music | Plot 2 | Demos | Index | Browse | More | WebCam
Contribute new seq. or comment | Format | Style Sheet | Transforms | Superseeker | Recent | More pages
The OEIS Community | Maintained by The OEIS Foundation Inc.

Last modified November 18 12:18 EST 2017. Contains 294891 sequences.