The OEIS is supported by the many generous donors to the OEIS Foundation.

 Hints (Greetings from The On-Line Encyclopedia of Integer Sequences!)
 A189804 Triangle read by rows: T(n,k) is the number of compositions of set {1, 2, ..., k} into exactly n blocks, each of size 1, 2 or 3 (n >= 0, 0 <= k <= 3*n). 1
 1, 0, 1, 1, 1, 0, 0, 2, 6, 14, 20, 20, 0, 0, 0, 6, 36, 150, 450, 1050, 1680, 1680, 0, 0, 0, 0, 24, 240, 1560, 7560, 29400, 90720, 218400, 369600, 369600, 0, 0, 0, 0, 0, 120, 1800, 16800, 117600, 667800, 3137400, 12243000, 38808000, 96096000, 168168000, 168168000 (list; graph; refs; listen; history; text; internal format)
 OFFSET 0,8 COMMENTS Row n has 3*n+1 entries. Column sums give A188896, row sums give A144422. - Adi Dani, May 14 2011 LINKS G. C. Greubel, Table of n, a(n) for the first 50 rows, flattened Moa Apagodu, David Applegate, N. J. A. Sloane, and Doron Zeilberger, Analysis of the Gift Exchange Problem, arXiv:1701.08394 [math.CO], 2017. David Applegate and N. J. A. Sloane, The Gift Exchange Problem, arXiv:0907.0513 [math.CO], 2009. FORMULA T(n, k) = k*T(n-1, k-1) + (1/2)*k*(k-1)*T(n-1, k-2) + (1/6)*k*(k-1)*(k-2)*T(n-1, k-3). E.g.f.: sum(n>=0, T(n, k)*x^k/k!) = (x+x^2/2+x^3/6)^k. EXAMPLE Triangle begins: [1] [0, 1, 1, 1] [0, 0, 2, 6, 14, 20, 20] [0, 0, 0, 6, 36, 150, 450, 1050, 1680, 1680] [0, 0, 0, 0, 24, 240, 1560, 7560, 29400, 90720, 218400, 369600, 369600] [0, 0, 0, 0, 0, 120, 1800, 16800, 117600, 667880, 3137400, 12243000, 3880800, 96096000, 168168000, 168168000] MAPLE T := proc(n, k) option remember; if n = k then 1; elif k < n then 0; elif n < 1 then 0; else =k *T(n - 1, k - 1) + (1/2)*k*(k - 1)*T(n - 1, k - 2)+ (1/6)*k* (k - 1)*(k - 2)*T(n - 1, k - 3); end if; end proc; for n from 0 to 12 do lprint([seq(T(n, k), k=0..3*n)]); od: MATHEMATICA Table[Sum[ n!/(2^(n + j - 2m)3^(m - j))Binomial[m, j]Binomial[j, n + 2j - 3m], {j, 0, 3m - n}], {m, 0, 5}, {n, 0, 3m}]//Flatten PROG (PARI) for(m=0, 7, for(n=0, 3*m, print1(sum(j=0, 3*m-n, (n!/(2^(n+j-2*m)*3^(m-j)))*binomial(m, j)*binomial(j, n+2*j-3*m)), ", "))) \\ G. C. Greubel, Jan 16 2018 CROSSREFS Sequence in context: A215807 A373437 A140525 * A308394 A246068 A032643 Adjacent sequences: A189801 A189802 A189803 * A189805 A189806 A189807 KEYWORD nonn,tabf AUTHOR Adi Dani, Apr 27 2011 EXTENSIONS Terms a(44) and a(47) corrected by G. C. Greubel, Jan 16 2018 STATUS approved

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

Last modified July 18 15:13 EDT 2024. Contains 374388 sequences. (Running on oeis4.)