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 A244135 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, 6, -2, 0, 48, -30, 9, 0, 500, -432, 252, -64, 0, 6480, -6860, 5760, -2880, 625, 0, 100842, -122880, 131220, -96000, 41250, -7776, 0, 1835008, -2480058, 3150000, -2981440, 1890000, -707616, 117649, 0, 38263752, -56000000, 81169704, -92897280, 76895000, -42674688, 14117880, -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. 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, 6, -2, 0, 48, -30, 9, 0, 500, -432, 252, -64, 0, 6480, -6860, 5760, -2880, 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. A244116, A244117, A244118, A244119, A244120, A244121, A244122, A244123, A244124, A244125, A244126, A244127, A244128, A244129, A244130, A244131, A244132, A244133, A244134, A244136, A244137, A244138, A244139, A244140, A244141, A244142, A244143. Sequence in context: A197844 A326825 A182639 * A120002 A296432 A171542 Adjacent sequences:  A244132 A244133 A244134 * A244136 A244137 A244138 KEYWORD sign,tabl AUTHOR Stanislav Sykora, Jun 22 2014 STATUS approved

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Last modified April 14 21:21 EDT 2021. Contains 342962 sequences. (Running on oeis4.)