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A244124 Triangle read by rows: coefficients T(n,k) of a binomial decomposition of 2^n-1 as Sum(k=0..n)T(n,k)*binomial(n,k). 28
0, 0, 1, 0, 2, -1, 0, 4, -3, 4, 0, 8, -9, 16, -27, 0, 16, -27, 64, -135, 256, 0, 32, -81, 256, -675, 1536, -3125, 0, 64, -243, 1024, -3375, 9216, -21875, 46656, 0, 128, -729, 4096, -16875, 55296, -153125, 373248, -823543, 0, 256, -2187, 16384, -84375, 331776, -1071875, 2985984, -7411887, 16777216 (list; table; graph; refs; listen; history; text; internal format)
OFFSET

0,5

COMMENTS

T(n,k)=(1-k)^(k-1)*(1+k)^(n-k) for k>0, while T(n,0)=0 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.(6), with b=1 and a=1.

EXAMPLE

The first rows of the triangle are:

0

0 1

0 2  -1

0 4  -3  4

0 8  -9  16 -27

0 16 -27 64 -135 256

PROG

(PARI) seq(nmax, b)={my(v, n, k, irow);

  v = vector((nmax+1)*(nmax+2)/2); v[1]=0;

  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)*(1+k*b)^(n-k); ); );

  return(v); }

  a=seq(100, 1)

CROSSREFS

Cf. A244116, A244117, A244118, A244119, A244120, A244121, A244122, A244123, A244125, A244126, A244127, A244128, A244129, A244130, A244131, A244132, A244133, A244134, A244135, A244136, A244137, A244138, A244139, A244140, A244141, A244142, A244143.

Sequence in context: A092488 A068527 A218599 * A183190 A276544 A214753

Adjacent sequences:  A244121 A244122 A244123 * A244125 A244126 A244127

KEYWORD

sign,tabl

AUTHOR

Stanislav Sykora, Jun 21 2014

STATUS

approved

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Last modified June 23 18:12 EDT 2017. Contains 288668 sequences.