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A244135 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, 6, -2, 0, 48, -30, 9, 0, 500, -432, 252, -64, 0, 6480, -6860, 5760, -2880, 625, 0, 100842, -122880, 131220, -96000, 41250, -7776, 0, 1835008, -2480058, 3150000, -2981440, 1890000, -707616, 117649, 0, 38263752, -56000000, 81169704, -92897280, 76895000, -42674688, 14117880, -2097152 (list; table; graph; refs; listen; history; text; internal format)
OFFSET

0,5

COMMENTS

T(n,k)=(-k)^(k-1)*(n+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.(13), with b=1.

EXAMPLE

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

1,

0, 1,

0, 6, -2,

0, 48, -30, 9,

0, 500, -432, 252, -64,

0, 6480, -6860, 5760, -2880, 625,

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

return(v); }

a=seq(100, 1);

CROSSREFS

Cf. A244116, A244117, A244118, A244119, A244120, A244121, A244122, A244123, A244124, A244125, A244126, A244127, A244128, A244129, A244130, A244131, A244132, A244133, A244134, A244136, A244137, A244138, A244139, A244140, A244141, A244142, A244143.

Sequence in context: A021621 A197844 A182639 * A120002 A171542 A284761

Adjacent sequences:  A244132 A244133 A244134 * A244136 A244137 A244138

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.