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A244141 Triangle read by rows: terms T(n,k) of a binomial decomposition of n*(-1)^n as Sum(k=0..n)T(n,k). 28
0, 0, -1, 0, 0, 2, 0, 0, 0, -3, 0, 0, 0, -12, 16, 0, 0, 0, -30, 160, -135, 0, 0, 0, -60, 960, -2430, 1536, 0, 0, 0, -105, 4480, -25515, 43008, -21875, 0, 0, 0, -168, 17920, -204120, 688128, -875000, 373248, 0, 0, 0, -252, 64512, -1377810, 8257536, -19687500, 20155392, -7411887 (list; table; graph; refs; listen; history; text; internal format)
OFFSET
0,6
COMMENTS
T(n,k)=(-1)^k*k*(k-2)^(n-2)*binomial(n,k) for k>1, while T(n,0)=0 and T(1,1)=-0^(n-1) 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.(21), with a=2, b=1.
EXAMPLE
First rows of the triangle, all summing up to n*(-1)^n:
0,
0, -1,
0, 0, 2,
0, 0, 0, -3,
0, 0, 0, -12, 16,
0, 0, 0, -30, 160, -135,
0, 0, 0, -60, 960, -2430, 1536,
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; if(n==1, v[irow+1]=-1, v[irow+1]=0);
for(k=2, n, v[irow+k]=(-1)^k*k*(k-2)^(n-2)*binomial(n, k); ); );
return(v); }
a=seq(100);
CROSSREFS
Sequence in context: A091227 A300715 A035444 * A152489 A143655 A173541
KEYWORD
sign,tabl
AUTHOR
Stanislav Sykora, Jun 23 2014
STATUS
approved

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Last modified June 20 18:00 EDT 2024. Contains 373532 sequences. (Running on oeis4.)