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A244116 Triangle read by rows: coefficients T(n,k) of a binomial decomposition of 1 as Sum(k=0..n)T(n,k)*binomial(n,k). 28
1, 0, 1, 0, 1, -1, 0, 1, -2, 4, 0, 1, -4, 12, -27, 0, 1, -8, 36, -108, 256, 0, 1, -16, 108, -432, 1280, -3125, 0, 1, -32, 324, -1728, 6400, -18750, 46656, 0, 1, -64, 972, -6912, 32000, -112500, 326592, -823543, 0, 1, -128, 2916, -27648, 160000, -675000, 2286144, -6588344, 16777216 (list; table; graph; refs; listen; history; text; internal format)
OFFSET

0,9

COMMENTS

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

LINKS

Stanislav Sykora, Table of n, 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.(4), with b=1.

EXAMPLE

The first rows of the triangle are:

1

0 1

0 1 -1

0 1 -2 4

0 1 -4 12 -27

0 1 -8 36 -108 256

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] = (1-k*b)^(k-1)*(k*b)^(n-k); );

  ); return(v); }

  a=seq(100, 1);

CROSSREFS

Cf. A244117, A244118, A244119, A244120, 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: A173004 A118343 A226031 * A138133 A005657 A009332

Adjacent sequences:  A244113 A244114 A244115 * A244117 A244118 A244119

KEYWORD

sign,tabl

AUTHOR

Stanislav Sykora, Jun 21 2014

STATUS

approved

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Last modified May 23 04:09 EDT 2017. Contains 286909 sequences.