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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. See eq.(4) with b=1.

EXAMPLE

The first few 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: A309148 A226031 A308460 * A138133 A302937 A005657

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 October 21 14:27 EDT 2019. Contains 328301 sequences. (Running on oeis4.)