A244120 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, 0, 0, 3, 6, 0, 0, 4, 32, 12, 0, 0, 5, 120, 180, 20, 0, 0, 6, 384, 1458, 768, 30, 0, 0, 7, 1120, 9072, 12096, 2800, 42, 0, 0, 8, 3072, 48600, 131072, 81000, 9216, 56, 0, 0, 9, 8064, 236196, 1152000, 1440000, 472392, 28224, 72, 0, 0, 10, 20480, 1071630, 8847360, 19531250, 13271040, 2500470, 81920, 90, 0

Offset

0,5

Comments

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

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.

Example

The first rows of the triangle are:
1
0 1
0 2   0
0 3   6   0
0 4  32  12  0
0 5 120 180 20 0

Prog

(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);

Crossrefs

Cf. A244116, A244117, A244118, A244119, A244121, A244122, A244123, A244124, A244125, A244126, A244127, A244128, A244129, A244130, A244131, A244132, A244133, A244134, A244135, A244136, A244137, A244138, A244139, A244140, A244141, A244142, A244143.

Sequence in context: A361100 A336309 A336255 * A277536 A348849 A351142

Adjacent sequences: A244117 A244118 A244119 * A244121 A244122 A244123

Keyword

nonn,tabl

Author

Stanislav Sykora, Jun 21 2014

Status

approved