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!)
A244140 Triangle read by rows: coefficients T(n,k) of a binomial decomposition of n*(-1)^n as Sum(k=0..n)T(n,k)*binomial(n,k). 28
0, 0, -1, 0, 0, 2, 0, 0, 0, -3, 0, 0, 0, -3, 16, 0, 0, 0, -3, 32, -135, 0, 0, 0, -3, 64, -405, 1536, 0, 0, 0, -3, 128, -1215, 6144, -21875, 0, 0, 0, -3, 256, -3645, 24576, -109375, 373248, 0, 0, 0, -3, 512, -10935, 98304, -546875, 2239488, -7411887, 0, 0, 0, -3, 1024, -32805, 393216, -2734375, 13436928, -51883209, 167772160 (list; table; graph; refs; listen; history; text; internal format)
OFFSET

0,6

COMMENTS

T(n,k)=(-1)^k*k*(k-2)^(n-2) for k>1, while T(n,0)=0 and T(1,1)=-0^(n-1) 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.(21), with a=2, b=1.

EXAMPLE

The first rows of the triangle are:

0,

0, -1,

0, 0, 2,

0, 0, 0, -3,

0, 0, 0, -3, 16,

0, 0, 0, -3, 32, -135,

0, 0, 0, -3, 64, -405, 1536,

0, 0, 0, -3, 128, -1215, 6144, -21875,

PROG

(PARI) seq(nmax)={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; if(n==1, v[irow+1]=-1, v[irow+1]=0);

for(k=2, n, v[irow+k]=(-1)^k*k*(k-2)^(n-2); ); );

return(v); }

a=seq(100);

CROSSREFS

Cf. A244116, A244117, A244118, A244119, A244120, A244121, A244122, A244123, A244124, A244125, A244126, A244127, A244128, A244129, A244130, A244131, A244132, A244133, A244134, A244135, A244136, A244137, A244138, A244139, A244141, A244142, A244143.

Sequence in context: A127647 A325458 A226728 * A091227 A300715 A035444

Adjacent sequences:  A244137 A244138 A244139 * A244141 A244142 A244143

KEYWORD

sign,tabl

AUTHOR

Stanislav Sykora, Jun 23 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 14 22:39 EDT 2021. Contains 342962 sequences. (Running on oeis4.)