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

 

Logo

Annual Appeal: Please make a donation to keep the OEIS running. In 2018 we replaced the server with a faster one, added 20000 new sequences, and reached 7000 citations (often saying "discovered thanks to the OEIS").
Other ways to donate

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
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, -432, 1280, -3125, 0, 1, -32, 324, -1728, 6400, -18750, 46656, 0, 1, -64, 972, -6912, 32000, -112500, 326592, -823543, 0, 1, -128, 2916, -27648, 160000, -675000, 2286144, -6588344, 16777216 (list; table; graph; refs; listen; history; text; internal format)
OFFSET

0,9

COMMENTS

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

LINKS

Stanislav Sykora, Table of n, 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.(4), with b=1.

EXAMPLE

The first rows of the triangle are:

1

0 1

0 1 -1

0 1 -2 4

0 1 -4 12 -27

0 1 -8 36 -108 256

PROG

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

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

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

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

  ); return(v); }

  a=seq(100, 1);

CROSSREFS

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.

Sequence in context: A173004 A118343 A226031 * A138133 A302937 A005657

Adjacent sequences:  A244113 A244114 A244115 * A244117 A244118 A244119

KEYWORD

sign,tabl

AUTHOR

Stanislav Sykora, Jun 21 2014

STATUS

approved

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 December 17 12:05 EST 2018. Contains 318201 sequences. (Running on oeis4.)