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A244141
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Triangle read by rows: terms T(n,k) of a binomial decomposition of n*(-1)^n as Sum(k=0..n)T(n,k).
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28
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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
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OFFSET
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0,6
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COMMENTS
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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.
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LINKS
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EXAMPLE
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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,
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PROG
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(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);
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CROSSREFS
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Cf. A244116, A244117, A244118, A244119, A244120, A244121, A244122, A244123, A244124, A244125, A244126, A244127, A244128, A244129, A244130, A244131, A244132, A244133, A244134, A244135, A244136, A244137, A244138, A244139, A244140, A244142, A244143.
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KEYWORD
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AUTHOR
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STATUS
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approved
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