A244121 Triangle read by rows: terms T(n,k) of a binomial decomposition of n^n as Sum(k=0..n)T(n,k).

1, 0, 1, 0, 4, 0, 0, 9, 18, 0, 0, 16, 192, 48, 0, 0, 25, 1200, 1800, 100, 0, 0, 36, 5760, 29160, 11520, 180, 0, 0, 49, 23520, 317520, 423360, 58800, 294, 0, 0, 64, 86016, 2721600, 9175040, 4536000, 258048, 448, 0, 0, 81, 290304, 19840464, 145152000, 181440000, 39680928, 1016064, 648, 0

Offset: 0

Author

Stanislav Sykora, Jun 21 2014

Keywords

• nonn
• tabl

Comments

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

Examples

			First rows of the triangle, all summing up to n^n:
1
0 1
0 4   0
0 9  18   0
0 16 192  48  0
0 25 1200 1800 100 0
		

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, A244122, 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)*binomial(n,k);););
  return(v);}
  a=seq(100,1);