login
This site is supported by donations to The OEIS Foundation.

 

Logo


Hints
(Greetings from The On-Line Encyclopedia of Integer Sequences!)
A244116 Triangle read by rows: coefficients T(n,k) of a binomial decomposition of 1 as Sum_{k=0..n} T(n,k)*binomial(n,k). 28

%I

%S 1,0,1,0,1,-1,0,1,-2,4,0,1,-4,12,-27,0,1,-8,36,-108,256,0,1,-16,108,

%T -432,1280,-3125,0,1,-32,324,-1728,6400,-18750,46656,0,1,-64,972,

%U -6912,32000,-112500,326592,-823543,0,1,-128,2916,-27648,160000,-675000,2286144,-6588344,16777216

%N Triangle read by rows: coefficients T(n,k) of a binomial decomposition of 1 as Sum_{k=0..n} T(n,k)*binomial(n,k).

%C T(n,k) = (1-k)^(k-1) * k^(n-k) for k>0, while T(n,0) = 0^n by convention.

%H Stanislav Sykora, <a href="/A244116/b244116.txt">Table of n, rows 0..100</a>

%H S. Sykora, <a href="http://dx.doi.org/10.3247/SL5Math14.004">An Abel's Identity and its Corollaries</a>, Stan's Library, Volume V, 2014. See eq.(4) with b=1.

%e The first few rows of the triangle are:

%e 1

%e 0 1

%e 0 1 -1

%e 0 1 -2 4

%e 0 1 -4 12 -27

%e 0 1 -8 36 -108 256

%e ...

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

%o v = vector((nmax+1)*(nmax+2)/2);v[1]=1;

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

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

%o );return(v);}

%o a=seq(100,1);

%Y Cf. 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, A244142, A244143.

%K sign,tabl

%O 0,9

%A _Stanislav Sykora_, Jun 21 2014

Lookup | Welcome | Wiki | Register | Music | Plot 2 | Demos | Index | Browse | More | WebCam
Contribute new seq. or comment | Format | Style Sheet | Transforms | Superseeker | Recent
The OEIS Community | Maintained by The OEIS Foundation Inc.

License Agreements, Terms of Use, Privacy Policy. .

Last modified November 22 13:47 EST 2019. Contains 329393 sequences. (Running on oeis4.)