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A244139 Triangle read by rows: terms T(n,k) of a binomial decomposition of n*(n-1) as Sum(k=0..n)T(n,k). 28
0, 0, 0, 0, 0, 2, 0, 0, 12, -6, 0, 0, 48, -72, 36, 0, 0, 160, -540, 720, -320, 0, 0, 480, -3240, 8640, -9600, 3750, 0, 0, 1344, -17010, 80640, -168000, 157500, -54432, 0, 0, 3584, -81648, 645120, -2240000, 3780000, -3048192, 941192, 0, 0, 9216, -367416, 4644864, -25200000, 68040000, -96018048, 67765824, -18874368 (list; table; graph; refs; listen; history; text; internal format)
OFFSET

0,6

COMMENTS

T(n,k)=k*(1-k)^(k-2)*k^(n-k)*binomial(n,k) for k>1, while T(n,0)=T(n,1)=0 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.(19), with a=1.

EXAMPLE

First rows of the triangle, all summing up to n*(n-1):

0,

0, 0,

0, 0, 2,

0, 0, 12, -6,

0, 0, 48, -72, 36,

0, 0, 160, -540, 720, -320,

0, 0, 480, -3240, 8640, -9600, 3750,

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; v[irow+1]=0;

  for(k=2, n, v[irow+k]=k*(1-k)^(k-2)*k^(n-k)*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, A244140, A244141, A244142, A244143.

Sequence in context: A000171 A054922 A289651 * A231031 A061848 A193294

Adjacent sequences:  A244136 A244137 A244138 * A244140 A244141 A244142

KEYWORD

sign,tabl

AUTHOR

Stanislav Sykora, Jun 22 2014

STATUS

approved

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