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A244121
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Triangle read by rows: terms T(n,k) of a binomial decomposition of n^n as Sum(k=0..n)T(n,k).
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28
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1, 0, 1, 0, 4, 0, 0, 9, 18, 0, 0, 16, 192, 48, 0, 0, 25, 1200, 1800, 100, 0, 0, 36, 5760, 29160, 11520, 180, 0, 0, 49, 23520, 317520, 423360, 58800, 294, 0, 0, 64, 86016, 2721600, 9175040, 4536000, 258048, 448, 0, 0, 81, 290304, 19840464, 145152000, 181440000, 39680928, 1016064, 648, 0
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OFFSET
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0,5
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COMMENTS
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T(n,k)=n*(n-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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EXAMPLE
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First rows of the triangle, all summing up to n^n:
1
0 1
0 4 0
0 9 18 0
0 16 192 48 0
0 25 1200 1800 100 0
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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]=n*(n-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, A244117, A244118, A244119, A244120, 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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