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A244138 Triangle read by rows: coefficients T(n,k) of a binomial decomposition of n*(n-1) as Sum(k=0..n)T(n,k)*binomial(n,k). 28
0, 0, 0, 0, 0, 2, 0, 0, 4, -6, 0, 0, 8, -18, 36, 0, 0, 16, -54, 144, -320, 0, 0, 32, -162, 576, -1600, 3750, 0, 0, 64, -486, 2304, -8000, 22500, -54432, 0, 0, 128, -1458, 9216, -40000, 135000, -381024, 941192, 0, 0, 256, -4374, 36864, -200000, 810000, -2667168, 7529536, -18874368 (list; table; graph; refs; listen; history; text; internal format)
OFFSET

0,6

COMMENTS

T(n,k)=k*(1-k)^(k-2)*k^(n-k) for k>1, while T(n,0)=T(n,1)=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.(19), with a=1.

EXAMPLE

The first rows of the triangle are:

0,

0, 0,

0, 0, 2,

0, 0, 4, -6,

0, 0, 8, -18, 36,

0, 0, 16, -54, 144, -320,

0, 0, 32, -162, 576, -1600, 3750,

PROG

(PARI) seq(nmax)={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; v[irow+1]=0;

  for(k=2, n, v[irow+k]=k*(1-k)^(k-2)*k^(n-k); ); );

return(v); }

a=seq(100);

CROSSREFS

Cf. A244116, A244117, A244118, A244119, A244120, A244121, A244122, A244123, A244124, A244125, A244126, A244127, A244128, A244129, A244130, A244131, A244132, A244133, A244134, A244135, A244136, A244137, A244139, A244140, A244141, A244142, A244143.

Sequence in context: A257813 A278280 A213370 * A284611 A282551 A333706

Adjacent sequences:  A244135 A244136 A244137 * A244139 A244140 A244141

KEYWORD

sign,tabl

AUTHOR

Stanislav Sykora, Jun 22 2014

STATUS

approved

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Last modified April 11 14:44 EDT 2021. Contains 342886 sequences. (Running on oeis4.)