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A244117
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Triangle read by rows: terms of a binomial decomposition of 1 as Sum(k=0..n)T(n,k).
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28
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1, 0, 1, 0, 2, -1, 0, 3, -6, 4, 0, 4, -24, 48, -27, 0, 5, -80, 360, -540, 256, 0, 6, -240, 2160, -6480, 7680, -3125, 0, 7, -672, 11340, -60480, 134400, -131250, 46656, 0, 8, -1792, 54432, -483840, 1792000, -3150000, 2612736, -823543, 0, 9, -4608, 244944, -3483648, 20160000, -56700000, 82301184, -59295096, 16777216
(list;
table;
graph;
refs;
listen;
history;
text;
internal format)
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OFFSET
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0,5
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COMMENTS
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T(n,k)=(1-k)^(k-1)*k^(n-k)*binomial(n,k) for k>0, while T(n,0)=0^n by convention.
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LINKS
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Stanislav Sykora, Table of n, a(n) for rows 0..100
S. Sykora, An Abel's Identity and its Corollaries, Stan's Library, Volume V, 2014, DOI 10.3247/SL5Math14.004. See eq.(4), with b=1.
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EXAMPLE
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First rows of the triangle, all summing up to 1:
1
0 1
0 2 -1
0 3 -6 4
0 4 -24 48 -27
0 5 -80 360 -540 256
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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)*binomial(n, k); );
); return(v); }
a=seq(100, 1);
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CROSSREFS
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Cf. A244116, A244118, 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.
Sequence in context: A077874 A286274 A230360 * A263426 A278882 A153007
Adjacent sequences: A244114 A244115 A244116 * A244118 A244119 A244120
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KEYWORD
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sign,tabl
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AUTHOR
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Stanislav Sykora, Jun 21 2014
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STATUS
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approved
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