login
The OEIS is supported by the many generous donors to the OEIS Foundation.

 

Logo
Hints
(Greetings from The On-Line Encyclopedia of Integer Sequences!)
A244123 Triangle read by rows: terms T(n,k) of a binomial decomposition of n^n as Sum(k=0..n)T(n,k). 28

%I #11 Jun 25 2014 09:38:55

%S 1,0,1,0,-4,8,0,9,-90,108,0,-16,576,-2352,2048,0,25,-2800,28800,

%T -72900,50000,0,-36,11520,-262440,1440000,-2635380,1492992,0,49,

%U -42336,1984500,-20870080,76204800,-109160142,52706752,0,-64,143360,-13172544,247726080,-1599416000,4337012736,-5103000000,2147483648

%N Triangle read by rows: terms T(n,k) of a binomial decomposition of n^n as Sum(k=0..n)T(n,k).

%C T(n,k)=n*(n+k)^(k-1)*(-k)^(n-k)*binomial(n,k) for k>0, while T(n,0)=0^n by convention.

%H Stanislav Sykora, <a href="/A244123/b244123.txt">Table of n, a(n) for rows 0..100</a>

%H S. Sykora, <a href="http://dx.doi.org/10.3247/SL5Math14.004">An Abel's Identity and its Corollaries</a>, Stan's Library, Volume V, 2014, DOI 10.3247/SL5Math14.004. See eq.(5), with b=-1.

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

%e 1

%e 0 1

%e 0 -4 8

%e 0, 9 -90 108

%e 0 -16 576 -2352 2048

%e 0, 25 -2800 28800 -72900 50000

%o (PARI) seq(nmax, b)={my(v, n, k, irow);

%o v = vector((nmax+1)*(nmax+2)/2); v[1]=1;

%o for(n=1, nmax, irow=1+n*(n+1)/2; v[irow]=0;

%o for(k=1, n, v[irow+k]=n*(n-k*b)^(k-1)*(k*b)^(n-k)*binomial(n, k); ); );

%o return(v); }

%o a=seq(100,-1);

%Y Cf. A244116, A244117, A244118, A244119, A244120, A244121, A244122, A244124, A244125, A244126, A244127, A244128, A244129, A244130, A244131, A244132, A244133, A244134, A244135, A244136, A244137, A244138, A244139, A244140, A244141, A244142, A244143.

%K sign,tabl

%O 0,5

%A _Stanislav Sykora_, Jun 21 2014

Lookup | Welcome | Wiki | Register | Music | Plot 2 | Demos | Index | Browse | More | WebCam
Contribute new seq. or comment | Format | Style Sheet | Transforms | Superseeker | Recents
The OEIS Community | Maintained by The OEIS Foundation Inc.

License Agreements, Terms of Use, Privacy Policy. .

Last modified March 29 06:34 EDT 2024. Contains 371265 sequences. (Running on oeis4.)