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A244140 Triangle read by rows: coefficients T(n,k) of a binomial decomposition of n*(-1)^n as Sum(k=0..n)T(n,k)*binomial(n,k). 28
0, 0, -1, 0, 0, 2, 0, 0, 0, -3, 0, 0, 0, -3, 16, 0, 0, 0, -3, 32, -135, 0, 0, 0, -3, 64, -405, 1536, 0, 0, 0, -3, 128, -1215, 6144, -21875, 0, 0, 0, -3, 256, -3645, 24576, -109375, 373248, 0, 0, 0, -3, 512, -10935, 98304, -546875, 2239488, -7411887, 0, 0, 0, -3, 1024, -32805, 393216, -2734375, 13436928, -51883209, 167772160 (list; table; graph; refs; listen; history; text; internal format)
OFFSET

0,6

COMMENTS

T(n,k)=(-1)^k*k*(k-2)^(n-2) for k>1, while T(n,0)=0 and T(1,1)=-0^(n-1) 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.(21), with a=2, b=1.

EXAMPLE

The first rows of the triangle are:

0,

0, -1,

0, 0, 2,

0, 0, 0, -3,

0, 0, 0, -3, 16,

0, 0, 0, -3, 32, -135,

0, 0, 0, -3, 64, -405, 1536,

0, 0, 0, -3, 128, -1215, 6144, -21875,

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; if(n==1, v[irow+1]=-1, v[irow+1]=0);

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

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, A244138, A244139, A244141, A244142, A244143.

Sequence in context: A127647 A226728 A140579 * A091227 A035444 A244141

Adjacent sequences:  A244137 A244138 A244139 * A244141 A244142 A244143

KEYWORD

sign,tabl

AUTHOR

Stanislav Sykora, Jun 23 2014

STATUS

approved

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Last modified July 25 20:28 EDT 2017. Contains 289797 sequences.