A244136 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, 1, 2, 0, 4, 2, 9, 0, 27, 8, 9, 64, 0, 256, 54, 36, 64, 625, 0, 3125, 512, 243, 256, 625, 7776, 0, 46656, 6250, 2304, 1728, 2500, 7776, 117649, 0, 823543, 93312, 28125, 16384, 16875, 31104, 117649, 2097152, 0, 16777216, 1647086, 419904, 200000, 160000, 209952, 470596, 2097152, 43046721

Offset

0,6

Comments

T(n,k)=(k)^(k-1)*(n-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.(13), with b=-1.

Example

The first rows of the triangle are:
1,
0, 1,
0, 1, 2,
0, 4, 2, 9,
0, 27, 8, 9, 64,
0, 256, 54, 36, 64, 625,

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]=(-k*b)^(k-1)*(n+k*b)^(n-k); ); );
return(v); }
a=seq(100, -1);

Crossrefs

Cf. A244116, A244117, A244118, A244119, A244120, A244121, A244122, A244123, A244124, A244125, A244126, A244127, A244128, A244129, A244130, A244131, A244132, A244133, A244134, A244135, A244137, A244138, A244139, A244140, A244141, A244142, A244143.

Sequence in context: A068773 A340692 A234312 * A338212 A337451 A352737

Adjacent sequences: A244133 A244134 A244135 * A244137 A244138 A244139

Keyword

nonn,tabl

Author

Stanislav Sykora, Jun 22 2014

Status

approved