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!)
 A244143 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, 18, -15, 0, 0, 108, -300, 196, 0, 0, 540, -3750, 6860, -3645, 0, 0, 2430, -37500, 144060, -196830, 87846, 0, 0, 10206, -328125, 2352980, -6200145, 6764142, -2599051, 0, 0, 40824, -2625000, 32941720, -148803480, 297622248, -270301304, 91125000 (list; table; graph; refs; listen; history; text; internal format)
 OFFSET 0,6 COMMENTS T(n,k)=(-1)^k*k*(2*k-1)^(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=1, b=2. EXAMPLE First rows of the triangle, all summing up to n: 0, 0, 1, 0, 0, 2, 0, 0, 18, -15, 0, 0, 108, -300, 196, 0, 0, 540, -3750, 6860, -3645, 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*(2*k-1)^(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, A244141, A244142. Sequence in context: A108474 A120582 A003784 * A066294 A230840 A209454 Adjacent sequences:  A244140 A244141 A244142 * A244144 A244145 A244146 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.

Last modified December 17 12:02 EST 2018. Contains 318200 sequences. (Running on oeis4.)