login
The OEIS Foundation is supported by donations from users of the OEIS and by a grant from the Simons Foundation.

 

Logo


Hints
(Greetings from The On-Line Encyclopedia of Integer Sequences!)
A244127 Triangle read by rows: terms T(n,k) of a binomial decomposition of 2^n-1 as Sum(k=0..n)T(n,k). 28
0, 0, 1, 0, 0, 3, 0, 0, -9, 16, 0, 0, 18, -128, 125, 0, 0, -30, 640, -1875, 1296, 0, 0, 45, -2560, 16875, -31104, 16807, 0, 0, -63, 8960, -118125, 435456, -588245, 262144, 0, 0, 84, -28672, 708750, -4644864, 11764900, -12582912, 4782969 (list; table; graph; refs; listen; history; text; internal format)
OFFSET

0,6

COMMENTS

T(n,k)=(1+k)^(k-1)*(1-k)^(n-k)*binomial(n,k) for k>0, while T(n,0)=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.(6), with b=-1 and a=1.

EXAMPLE

First rows of the triangle, all summing up to 2^n-1:

0,

0, 1,

0, 0, 3,

0, 0, -9, 16,

0, 0, 18, -128, 125,

0, 0, -30, 640, -1875, 1296,

PROG

(PARI) seq(nmax, b)={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;

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

  return(v); }

  a=seq(100, -1)

CROSSREFS

Cf. A244116, A244117, A244118, A244119, A244120, A244121, A244122, A244123, A244124, A244125, A244126, A244128, A244129, A244130, A244131, A244132, A244133, A244134, A244135, A244136, A244137, A244138, A244139, A244140, A244141, A244142, A244143.

Sequence in context: A104751 A265828 A177016 * A342312 A123474 A321711

Adjacent sequences:  A244124 A244125 A244126 * A244128 A244129 A244130

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 April 11 14:58 EDT 2021. Contains 342886 sequences. (Running on oeis4.)