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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: A335461 A294411 A274390 * A016584 A293961 A112899

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 April 10 19:06 EDT 2021. Contains 342853 sequences. (Running on oeis4.)