A244135 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, 6, -2, 0, 48, -30, 9, 0, 500, -432, 252, -64, 0, 6480, -6860, 5760, -2880, 625, 0, 100842, -122880, 131220, -96000, 41250, -7776, 0, 1835008, -2480058, 3150000, -2981440, 1890000, -707616, 117649, 0, 38263752, -56000000, 81169704, -92897280, 76895000, -42674688, 14117880, -2097152

Offset

0,5

Comments

T(n,k)=(-k)^(k-1)*(n+k)^(n-k)*binomial(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

First rows of the triangle, all summing up to n^n:
1,
0, 1,
0, 6, -2,
0, 48, -30, 9,
0, 500, -432, 252, -64,
0, 6480, -6860, 5760, -2880, 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)*binomial(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, A244136, A244137, A244138, A244139, A244140, A244141, A244142, A244143.

Sequence in context: A197844 A326825 A182639 * A120002 A296432 A171542

Adjacent sequences: A244132 A244133 A244134 * A244136 A244137 A244138

Keyword

sign,tabl

Author

Stanislav Sykora, Jun 22 2014

Status

approved