A244134 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, 3, -2, 0, 16, -10, 9, 0, 125, -72, 63, -64, 0, 1296, -686, 576, -576, 625, 0, 16807, -8192, 6561, -6400, 6875, -7776, 0, 262144, -118098, 90000, -85184, 90000, -101088, 117649, 0, 4782969, -2000000, 1449459, -1327104, 1373125, -1524096, 1764735, -2097152

Offset

0,5

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, 3, -2,
0, 16, -10, 9,
0, 125, -72, 63, -64,
0, 1296, -686, 576, -576, 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, A244135, A244136, A244137, A244138, A244139, A244140, A244141, A244142, A244143.

Sequence in context: A282423 A111541 A371025 * A105629 A085075 A321518

Adjacent sequences: A244131 A244132 A244133 * A244135 A244136 A244137

Keyword

sign,tabl

Author

Stanislav Sykora, Jun 22 2014

Status

approved