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

 

Logo


Hints
(Greetings from The On-Line Encyclopedia of Integer Sequences!)
A244132 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, -2, 9, 0, 0, 2, -18, 64, 0, 0, -2, 36, -192, 625, 0, 0, 2, -72, 576, -2500, 7776, 0, 0, -2, 144, -1728, 10000, -38880, 117649, 0, 0, 2, -288, 5184, -40000, 194400, -705894, 2097152, 0, 0, -2, 576, -15552, 160000, -972000, 4235364, -14680064, 43046721 (list; table; graph; refs; listen; history; text; internal format)
OFFSET

0,6

COMMENTS

T(n,k)=(k)^(k-1)*(1-k)^(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.(12), with b=-1.

EXAMPLE

The first rows of the triangle are:

0,

0, 1,

0, 0, 2,

0, 0, -2, 9,

0, 0, 2, -18, 64,

0, 0, -2, 36, -192, 625,

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]=(-k*b)^(k-1)*(1+k*b)^(n-k); ); );

return(v); }

a=seq(100, -1);

CROSSREFS

Cf. A244116, A244117, A244118, A244119, A244120, A244121, A244122, A244123, A244124, A244125, A244126, A244127, A244128, A244129, A244130, A244131, A244133, A244134, A244135, A244136, A244137, A244138, A244139, A244140, A244141, A244142, A244143.

Sequence in context: A202496 A165664 A019263 * A169776 A240766 A265494

Adjacent sequences:  A244129 A244130 A244131 * A244133 A244134 A244135

KEYWORD

sign,tabl

AUTHOR

Stanislav Sykora, Jun 22 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 | More pages
The OEIS Community | Maintained by The OEIS Foundation Inc.

License Agreements, Terms of Use, Privacy Policy .

Last modified May 22 16:19 EDT 2017. Contains 286882 sequences.