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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

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Last modified August 17 23:58 EDT 2017. Contains 290682 sequences.