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 A244137 Triangle read by rows: terms T(n,k) of a binomial decomposition of n^n as Sum(k=0..n)T(n,k). 28
 1, 0, 1, 0, 2, 2, 0, 12, 6, 9, 0, 108, 48, 36, 64, 0, 1280, 540, 360, 320, 625, 0, 18750, 7680, 4860, 3840, 3750, 7776, 0, 326592, 131250, 80640, 60480, 52500, 54432, 117649, 0, 6588344, 2612736, 1575000, 1146880, 945000, 870912, 941192, 2097152 (list; table; graph; refs; listen; history; text; internal format)
 OFFSET 0,5 COMMENTS T(n,k)=(k)^(k-1)*(n-k)^(n-k)*binomial(n,k) for k>0, while T(n,0)=0^n by convention. There are many binomial decompositions of n^n, some with all terms positive like this one (see A243203). However, for every n, the terms corresponding to k=1..n in this one are exceptionally similar in value (at least on log scale). LINKS 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.(13), with b=-1. EXAMPLE First rows of the triangle, all summing up to n^n: 1, 0, 1, 0, 2, 2, 0, 12, 6, 9, 0, 108, 48, 36, 64, 0, 1280, 540, 360, 320, 625, PROG (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]=(-k*b)^(k-1)*(n+k*b)^(n-k)*binomial(n, k); ); ); return(v); } a=seq(100, -1); CROSSREFS Cf. A243203, A244116, A244117, A244118, A244119, A244120, A244121, A244122, A244123, A244124, A244125, A244126, A244127, A244128, A244129, A244130, A244131, A244132, A244133, A244134, A244135, A244136, A244138, A244139, A244140, A244141, A244142, A244143. Sequence in context: A285783 A364240 A117270 * A354127 A181389 A091466 Adjacent sequences: A244134 A244135 A244136 * A244138 A244139 A244140 KEYWORD nonn,tabl AUTHOR Stanislav Sykora, Jun 22 2014 STATUS approved

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Last modified November 30 11:40 EST 2023. Contains 367460 sequences. (Running on oeis4.)