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 A243202 Coefficients of a particular decomposition of N^N in terms of binomial coefficients. 2
 0, 0, 1, 0, 1, 2, 0, 3, 4, 6, 0, 16, 16, 18, 24, 0, 125, 100, 90, 96, 120, 0, 1296, 864, 648, 576, 600, 720, 0, 16807, 9604, 6174, 4704, 4200, 4320, 5040, 0, 262144, 131072, 73728, 49152, 38400, 34560, 35280, 40320, 0 (list; table; graph; refs; listen; history; text; internal format)
 OFFSET 0,6 COMMENTS a(n) is an element in the triangle of coefficients c(N,j), N = 0,1,2,3,... denoting a row, and j = 0,1,2,...r, specified numerically by the formula below. For any row N, Sum(j=0..N)(c(N,j)*binomial(N,j)) = N^N. Note that all rows start with 0, which makes them easily recognizable. It is believed that keeping the zero terms is preferable because it makes the summation run over all admissible j's in the binomial. 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, 1, 2 3 0, 3, 4, 6 4 0, 16, 16, 18, 24 5 0, 125, 100, 90, 96, 120 6 0, 1296, 864, 648, 576, 600, 720 7 0, 16807, 9604, 6174, 4704, 4200, 4320, 5040 8 0, 262144, 131072, 73728, 49152, 38400, 34560, 35280, 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); ); );   return(v); } CROSSREFS Cf. A243203. Sequence in context: A109921 A139637 A307734 * A257136 A258871 A283528 Adjacent sequences:  A243199 A243200 A243201 * A243203 A243204 A243205 KEYWORD nonn,easy,tabl AUTHOR Stanislav Sykora, Jun 01 2014 STATUS approved

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Last modified May 7 01:03 EDT 2021. Contains 343629 sequences. (Running on oeis4.)