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!)
A244141 Triangle read by rows: terms T(n,k) of a binomial decomposition of n*(-1)^n as Sum(k=0..n)T(n,k). 28
0, 0, -1, 0, 0, 2, 0, 0, 0, -3, 0, 0, 0, -12, 16, 0, 0, 0, -30, 160, -135, 0, 0, 0, -60, 960, -2430, 1536, 0, 0, 0, -105, 4480, -25515, 43008, -21875, 0, 0, 0, -168, 17920, -204120, 688128, -875000, 373248, 0, 0, 0, -252, 64512, -1377810, 8257536, -19687500, 20155392, -7411887 (list; table; graph; refs; listen; history; text; internal format)
OFFSET

0,6

COMMENTS

T(n,k)=(-1)^k*k*(k-2)^(n-2)*binomial(n,k) 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

First rows of the triangle, all summing up to n*(-1)^n:

0,

0, -1,

0, 0, 2,

0, 0, 0, -3,

0, 0, 0, -12, 16,

0, 0, 0, -30, 160, -135,

0, 0, 0, -60, 960, -2430, 1536,

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)*binomial(n, k); ); );

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, A244140, A244142, A244143.

Sequence in context: A091227 A300715 A035444 * A152489 A143655 A173541

Adjacent sequences:  A244138 A244139 A244140 * A244142 A244143 A244144

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 11 15:49 EDT 2021. Contains 342886 sequences. (Running on oeis4.)