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.
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
KEYWORD
nonn,tabl
AUTHOR
Stanislav Sykora, Jun 01 2014
STATUS
approved