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A244121 Triangle read by rows: terms T(n,k) of a binomial decomposition of n^n as Sum(k=0..n)T(n,k). 28
1, 0, 1, 0, 4, 0, 0, 9, 18, 0, 0, 16, 192, 48, 0, 0, 25, 1200, 1800, 100, 0, 0, 36, 5760, 29160, 11520, 180, 0, 0, 49, 23520, 317520, 423360, 58800, 294, 0, 0, 64, 86016, 2721600, 9175040, 4536000, 258048, 448, 0, 0, 81, 290304, 19840464, 145152000, 181440000, 39680928, 1016064, 648, 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)*binomial(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

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

1

0 1

0 4   0

0 9  18   0

0 16 192  48  0

0 25 1200 1800 100 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)*binomial(n, k); ); );

  return(v); }

  a=seq(100, 1);

CROSSREFS

Cf. A244116, A244117, A244118, A244119, A244120, 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: A127733 A330379 A249035 * A127774 A127319 A272626

Adjacent sequences:  A244118 A244119 A244120 * A244122 A244123 A244124

KEYWORD

nonn,tabl

AUTHOR

Stanislav Sykora, Jun 21 2014

STATUS

approved

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Last modified April 10 19:06 EDT 2021. Contains 342853 sequences. (Running on oeis4.)