A244122 Triangle read by rows: coefficients T(n,k) of a binomial decomposition of n^n as Sum(k=0..n)T(n,k)*binomial(n,k).

1, 0, 1, 0, -2, 8, 0, 3, -30, 108, 0, -4, 96, -588, 2048, 0, 5, -280, 2880, -14580, 50000, 0, -6, 768, -13122, 96000, -439230, 1492992, 0, 7, -2016, 56700, -596288, 3628800, -15594306, 52706752, 0, -8, 5120, -235224, 3538944, -28561000, 154893312, -637875000, 2147483648, 0

Offset: 0

Author

Stanislav Sykora, Jun 21 2014

Keywords

• sign
• tabl

Comments

T(n,k)=n*(n+k)^(k-1)*(-k)^(n-k) for k>0, while T(n,0)=0^n by convention.

Examples

			The first rows of the triangle are:
1
0  1
0 -2    8
0  3  -30  108
0 -4   96 -588   2048
0  5 -280 2880 -14580 50000
		

Links

• Stanislav Sykora, Table of n, a(n) for rows 0..100
• S. Sykora, An Abel's Identity and its Corollaries, Stan's Library, Volume V, 2014, DOI 10.3247/SL5Math14.004. See eq.(5), with b=-1.

Crossrefs

Cf. A244116, A244117, A244118, A244119, A244120, A244121, A244123, A244124, A244125, A244126, A244127, A244128, A244129, A244130, A244131, A244132, A244133, A244134, A244135, A244136, A244137, A244138, A244139, A244140, A244141, A244142, A244143.

Programs

PARI

seq(nmax, b)={my(v, n, k, irow);
  v = vector((nmax+1)*(nmax+2)/2); v[1]=1;
  for(n=1, nmax, irow=1+n*(n+1)/2; v[irow]=0;
  for(k=1, n, v[irow+k] = n*(n-k*b)^(k-1)*(k*b)^(n-k); ); );
  return(v); }
  a=seq(100,-1);