login
This site is supported by donations to The OEIS Foundation.

 

Logo


Hints
(Greetings from The On-Line Encyclopedia of Integer Sequences!)
A244120 Triangle read by rows: coefficients T(n,k) of a binomial decomposition of n^n as Sum(k=0..n)T(n,k)*binomial(n,k). 28
1, 0, 1, 0, 2, 0, 0, 3, 6, 0, 0, 4, 32, 12, 0, 0, 5, 120, 180, 20, 0, 0, 6, 384, 1458, 768, 30, 0, 0, 7, 1120, 9072, 12096, 2800, 42, 0, 0, 8, 3072, 48600, 131072, 81000, 9216, 56, 0, 0, 9, 8064, 236196, 1152000, 1440000, 472392, 28224, 72, 0, 0, 10, 20480, 1071630, 8847360, 19531250, 13271040, 2500470, 81920, 90, 0 (list; table; graph; refs; listen; history; text; internal format)
OFFSET

0,5

COMMENTS

T(n,k)=n*(n-k)^(k-1)*k^(n-k) for k>0, while T(n,0)=0^n 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.(5), with b=1.

EXAMPLE

The first rows of the triangle are:

1

0 1

0 2   0

0 3   6   0

0 4  32  12  0

0 5 120 180 20 0

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] = n*(n-k*b)^(k-1)*(k*b)^(n-k); ); );

  return(v); }

  a=seq(100, 1);

CROSSREFS

Cf. A244116, A244117, A244118, A244119, 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: A053653 A262174 A064146 * A277536 A269159 A216394

Adjacent sequences:  A244117 A244118 A244119 * A244121 A244122 A244123

KEYWORD

nonn,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 | More pages
The OEIS Community | Maintained by The OEIS Foundation Inc.

License Agreements, Terms of Use, Privacy Policy .

Last modified June 28 16:56 EDT 2017. Contains 288839 sequences.