This site is supported by donations to The OEIS Foundation.

 Annual Appeal: Please make a donation to keep the OEIS running. In 2018 we replaced the server with a faster one, added 20000 new sequences, and reached 7000 citations (often saying "discovered thanks to the OEIS"). Other ways to donate

 Hints (Greetings from The On-Line Encyclopedia of Integer Sequences!)
 A244118 Triangle read by rows: coefficients T(n,k) of a binomial decomposition of 1 as Sum(k=0..n)T(n,k)*binomial(n,k). 28
 1, 0, 1, 0, -1, 3, 0, 1, -6, 16, 0, -1, 12, -48, 125, 0, 1, -24, 144, -500, 1296, 0, -1, 48, -432, 2000, -6480, 16807, 0, 1, -96, 1296, -8000, 32400, -100842, 262144, 0, -1, 192, -3888, 32000, -162000, 605052, -1835008, 4782969, 0, 1, -384, 11664, -128000, 810000, -3630312, 12845056, -38263752, 100000000 (list; table; graph; refs; listen; history; text; internal format)
 OFFSET 0,6 COMMENTS T(n,k)=(1+k)^(k-1)*(-k)^(n-k) for k>0, while T(n,0)=0^n. 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.(4), with b=-1. EXAMPLE The first rows of the triangle are: 1 0  1 0 -1   3 0  1  -6  16 0 -1  12 -48  125 0  1 -24 144 -500 1296 PROG (PARI) seq(nmax, b)={my(v, n, k, irow);   v = vector((nmax+1)*(nmax+2)/2); v[1]=1;   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)*(k*b)^(n-k); );   ); return(v); }   a=seq(100, -1); CROSSREFS Cf. A244116, A244117, A244119, A244120, A244121, A244122, A244123, A244124, A244125, A244126, A244127, A244128, A244129, A244130, A244131, A244132, A244133, A244134, A244135, A244136, A244137, A244138, A244139, A244140, A244141, A244142, A244143. Sequence in context: A243984 A100485 A143397 * A273155 A208345 A216807 Adjacent sequences:  A244115 A244116 A244117 * A244119 A244120 A244121 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.

Last modified December 16 07:12 EST 2018. Contains 318158 sequences. (Running on oeis4.)