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A244142 Triangle read by rows: coefficients T(n,k) of a binomial decomposition of n as Sum(k=0..n)T(n,k)*binomial(n,k). 28
0, 0, 1, 0, 0, 2, 0, 0, 6, -15, 0, 0, 18, -75, 196, 0, 0, 54, -375, 1372, -3645, 0, 0, 162, -1875, 9604, -32805, 87846, 0, 0, 486, -9375, 67228, -295245, 966306, -2599051, 0, 0, 1458, -46875, 470596, -2657205, 10629366, -33787663, 91125000 (list; table; graph; refs; listen; history; text; internal format)
OFFSET

0,6

COMMENTS

T(n,k)=(-1)^k*k*(2*k-1)^(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=1, b=2.

EXAMPLE

The first rows of the triangle are:

0,

0, 1,

0, 0, 2,

0, 0, 6, -15,

0, 0, 18, -75, 196,

0, 0, 54, -375, 1372, -3645

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*(2*k-1)^(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, A244140, A244141, A244143.

Sequence in context: A137250 A329290 A244133 * A161800 A246608 A100344

Adjacent sequences:  A244139 A244140 A244141 * A244143 A244144 A244145

KEYWORD

sign,tabl

AUTHOR

Stanislav Sykora, Jun 23 2014

STATUS

approved

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Last modified April 11 12:38 EDT 2021. Contains 342886 sequences. (Running on oeis4.)