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A244128
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Triangle read by rows: coefficients T(n,k) of a binomial decomposition of 0^(n-1) as Sum(k=0..n)T(n,k)*binomial(n,k).
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28
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0, 1, 0, 1, -2, 0, 1, -4, 9, 0, 1, -8, 27, -64, 0, 1, -16, 81, -256, 625, 0, 1, -32, 243, -1024, 3125, -7776, 0, 1, -64, 729, -4096, 15625, -46656, 117649, 0, 1, -128, 2187, -16384, 78125, -279936, 823543, -2097152, 0, 1, -256, 6561, -65536, 390625, -1679616, 5764801, -16777216, 43046721
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OFFSET
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1,5
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COMMENTS
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T(n,k)=(-k)^(k-1)*k^(n-k) for k>0, while T(n,0)=0 by convention. The flattened triangle start with row 1, coefficient T(1,0).
Resembles A076014, but with added powers of 0, and with sign-alternating columns.
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LINKS
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EXAMPLE
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The first rows of the triangle (starting at n=1):
0, 1,
0, 1, -2,
0, 1, -4, 9,
0, 1, -8, 27, -64,
0, 1, -16, 81, -256, 625,
0, 1, -32, 243, -1024, 3125, -7776,
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PROG
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(PARI) seq(nmax, b)={my(v, n, k, irow);
v = vector((nmax+1)*(nmax+2)/2-1);
for(n=1, nmax, irow=n*(n+1)/2; v[irow]=0;
for(k=1, n, v[irow+k]=(-1)^(k-1)*(k*b)^(n-1); ); );
return(v); }
a=seq(100, 1);
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CROSSREFS
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Cf. A076014, A244116, A244117, A244118, A244119, A244120, A244121, A244122, A244123, A244124, A244125, A244126, A244127, A244129, A244130, A244131, A244132, A244133, A244134, A244135, A244136, A244137, A244138, A244139, A244140, A244141, A244142, A244143.
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KEYWORD
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sign,tabf
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AUTHOR
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STATUS
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approved
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