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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
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
Sequence in context: A197844 A326825 A182639 * A120002 A296432 A171542
KEYWORD
sign,tabl
AUTHOR
Stanislav Sykora, Jun 22 2014
STATUS
approved

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Last modified June 23 22:09 EDT 2024. Contains 373661 sequences. (Running on oeis4.)