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

 

Logo
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
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
Sequence in context: A079194 A179198 A117739 * A268652 A111810 A019265
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 | Recents
The OEIS Community | Maintained by The OEIS Foundation Inc.

License Agreements, Terms of Use, Privacy Policy. .

Last modified March 19 06:05 EDT 2024. Contains 370952 sequences. (Running on oeis4.)