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A244128 Triangle read by rows: coefficients T(n,k) of a binomial decomposition of 0^(n-1) as Sum(k=0..n)T(n,k)*binomial(n,k). 28
0, 1, 0, 1, -2, 0, 1, -4, 9, 0, 1, -8, 27, -64, 0, 1, -16, 81, -256, 625, 0, 1, -32, 243, -1024, 3125, -7776, 0, 1, -64, 729, -4096, 15625, -46656, 117649, 0, 1, -128, 2187, -16384, 78125, -279936, 823543, -2097152, 0, 1, -256, 6561, -65536, 390625, -1679616, 5764801, -16777216, 43046721 (list; table; graph; refs; listen; history; text; internal format)
OFFSET

1,5

COMMENTS

T(n,k)=(-k)^(k-1)*k^(n-k) for k>0, while T(n,0)=0 by convention. The flattened triangle start with row 1, coefficient T(1,0).

Resembles A076014, but with added powers of 0, and with sign-alternating columns.

LINKS

Stanislav Sykora, Table of n, a(n) for rows 1..100

S. Sykora, An Abel's Identity and its Corollaries, Stan's Library, Volume V, 2014, DOI 10.3247/SL5Math14.004. See eq.(11), with b=1.

EXAMPLE

The first rows of the triangle (starting at n=1):

0, 1,

0, 1, -2,

0, 1, -4, 9,

0, 1, -8, 27, -64,

0, 1, -16, 81, -256, 625,

0, 1, -32, 243, -1024, 3125, -7776,

PROG

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

v = vector((nmax+1)*(nmax+2)/2-1);

for(n=1, nmax, irow=n*(n+1)/2; v[irow]=0;

  for(k=1, n, v[irow+k]=(-1)^(k-1)*(k*b)^(n-1); ); );

return(v); }

a=seq(100, 1);

CROSSREFS

Cf. A076014, A244116, A244117, A244118, A244119, A244120, A244121, A244122, A244123, A244124, A244125, A244126, A244127, A244129, A244130, A244131, A244132, A244133, A244134, A244135, A244136, A244137, A244138, A244139, A244140, A244141, A244142, A244143.

Sequence in context: A287318 A173003 A274390 * A016584 A112899 A212808

Adjacent sequences:  A244125 A244126 A244127 * A244129 A244130 A244131

KEYWORD

sign,tabl

AUTHOR

Stanislav Sykora, Jun 22 2014

STATUS

approved

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Last modified May 26 03:22 EDT 2017. Contains 287073 sequences.