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

 

Logo


Hints
(Greetings from The On-Line Encyclopedia of Integer Sequences!)
A244133 Triangle read by rows: terms T(n,k) of a binomial decomposition of n as Sum(k=0..n)T(n,k). 28
0, 0, 1, 0, 0, 2, 0, 0, -6, 9, 0, 0, 12, -72, 64, 0, 0, -20, 360, -960, 625, 0, 0, 30, -1440, 8640, -15000, 7776, 0, 0, -42, 5040, -60480, 210000, -272160, 117649, 0, 0, 56, -16128, 362880, -2240000, 5443200, -5647152, 2097152, 0, 0, -72, 48384, -1959552, 20160000, -81648000, 152473104, -132120576, 43046721 (list; table; graph; refs; listen; history; text; internal format)
OFFSET

0,6

COMMENTS

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

EXAMPLE

First rows of the triangle, all summing up to n:

0,

0, 1,

0, 0, 2,

0, 0, -6, 9,

0, 0, 12, -72, 64,

0, 0, -20, 360, -960, 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)*binomial(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, A244132, A244134, A244135, A244136, A244137, A244138, A244139, A244140, A244141, A244142, A244143.

Sequence in context: A231063 A230250 A137250 * A244142 A161800 A246608

Adjacent sequences:  A244130 A244131 A244132 * A244134 A244135 A244136

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 August 16 08:52 EDT 2017. Contains 290623 sequences.