The OEIS Foundation is supported by donations from users of the OEIS and by a grant from the Simons Foundation.

 Hints (Greetings from The On-Line Encyclopedia of Integer Sequences!)
 A243203 Terms of a particular integer decomposition of N^N. 4
 0, 0, 1, 0, 2, 2, 0, 9, 12, 6, 0, 64, 96, 72, 24, 0, 625, 1000, 900, 480, 120, 0, 7776, 12960, 12960, 8640, 3600, 720, 0, 117649, 201684, 216090, 164640, 88200, 30240, 5040, 0, 2097152, 3670016, 4128768, 3440640, 2150400, 967680, 282240, 40320, 0 (list; table; graph; refs; listen; history; text; internal format)
 OFFSET 0,5 COMMENTS a(n) is an element in the triangle of terms t(N,j) = c(N,j)*binomial(N,j), N = 0,1,2,3,... denoting a row, and j = 0,1,2,...r. The coefficients c(N,j) are specified numerically by the formula below. Note that all rows start with 0, which makes them easily recognizable. The sum of every row is N^N. Though the original contexts are different, this triangle matches that of A066324 except for row 0, and for the zero term of each row. On this point, see the comment in A243202. LINKS Stanislav Sykora, Table of n, a(n) for rows 0..100, flattened S. Sykora, A Random Mapping Statistics and a Related Identity, Stan's Library, Volume V, June 2014. FORMULA c(N,j)=N^(N-j)*(j/N)*j!  for  N>0 and 0<=j<=N, and c(N,j)=0 otherwise. EXAMPLE The first rows of the triangle are (first item is the row number N): 0 0 1 0, 1 2 0, 2, 2 3 0, 9, 12, 6 4 0, 64, 96, 72, 24 5 0, 625, 1000, 900, 480, 120 6 0, 7776, 12960, 12960, 8640, 3600, 720 7 0, 117649, 201684, 216090, 164640, 88200, 30240, 5040 8 0, 2097152, 3670016, 4128768, 3440640, 2150400, 967680, 282240, 40320 PROG (PARI) A243202(maxrow) = {   my(v, n, j, irow, f); v = vector((maxrow+1)*(maxrow+2)/2);   for(n=1, maxrow, irow=1+n*(n+1)/2; v[irow]=0; f=1;   for(j=1, n, f *= j; v[irow+j] = j*f*n^(n-j-1)*binomial(n, j); ); );   return(v); } CROSSREFS Cf. A066324, A243202. Sequence in context: A079194 A179198 A117739 * A268652 A111810 A019265 Adjacent sequences:  A243200 A243201 A243202 * A243204 A243205 A243206 KEYWORD nonn,tabl AUTHOR Stanislav Sykora, Jun 01 2014 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
The OEIS Community | Maintained by The OEIS Foundation Inc.

Last modified May 26 08:39 EDT 2020. Contains 334620 sequences. (Running on oeis4.)