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A244122 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). 28
1, 0, 1, 0, -2, 8, 0, 3, -30, 108, 0, -4, 96, -588, 2048, 0, 5, -280, 2880, -14580, 50000, 0, -6, 768, -13122, 96000, -439230, 1492992, 0, 7, -2016, 56700, -596288, 3628800, -15594306, 52706752, 0, -8, 5120, -235224, 3538944, -28561000, 154893312, -637875000, 2147483648, 0 (list; table; graph; refs; listen; history; text; internal format)
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    8

0  3  -30  108

0 -4   96 -588   2048

0  5 -280 2880 -14580 50000

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, A244120, A244121, A244123, A244124, A244125, A244126, A244127, A244128, A244129, A244130, A244131, A244132, A244133, A244134, A244135, A244136, A244137, A244138, A244139, A244140, A244141, A244142, A244143.

Sequence in context: A016593 A020818 A197252 * A021785 A136664 A086728

Adjacent sequences:  A244119 A244120 A244121 * A244123 A244124 A244125

KEYWORD

sign,tabl

AUTHOR

Stanislav Sykora, Jun 21 2014

STATUS

approved

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Last modified August 22 12:56 EDT 2017. Contains 290948 sequences.