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A244118
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Triangle read by rows: coefficients T(n,k) of a binomial decomposition of 1 as Sum_{k=0..n} T(n,k)*binomial(n,k).
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28
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1, 0, 1, 0, -1, 3, 0, 1, -6, 16, 0, -1, 12, -48, 125, 0, 1, -24, 144, -500, 1296, 0, -1, 48, -432, 2000, -6480, 16807, 0, 1, -96, 1296, -8000, 32400, -100842, 262144, 0, -1, 192, -3888, 32000, -162000, 605052, -1835008, 4782969, 0, 1, -384, 11664, -128000, 810000, -3630312, 12845056, -38263752, 100000000
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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-1)*(-k)^(n-k) for k>0, where T(n,0) = 0^n.
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LINKS
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EXAMPLE
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The first rows of the triangle are:
1
0 1
0 -1 3
0 1 -6 16
0 -1 12 -48 125
0 1 -24 144 -500 1296
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PROG
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(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] = (1-k*b)^(k-1)*(k*b)^(n-k); );
); return(v); }
a=seq(100, -1);
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CROSSREFS
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Cf. A244116, A244117, A244119, A244120, A244121, A244122, A244123, A244124, A244125, A244126, A244127, A244128, A244129, A244130, A244131, A244132, A244133, A244134, A244135, A244136, A244137, A244138, A244139, A244140, A244141, 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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