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 A055858 Coefficient triangle for certain polynomials. 11
 1, 1, 2, 4, 9, 6, 27, 64, 48, 36, 256, 625, 500, 400, 320, 3125, 7776, 6480, 5400, 4500, 3750, 46656, 117649, 100842, 86436, 74088, 63504, 54432, 823543, 2097152, 1835008, 1605632, 1404928, 1229312, 1075648, 941192, 16777216, 43046721 (list; table; graph; refs; listen; history; text; internal format)
 OFFSET 0,3 COMMENTS The coefficients of the partner polynomials are found in triangle A055864. LINKS FORMULA a(n, m)=0 if n < m; a(0, 0)=1, a(n, 0) = n^n, n >= 1, a(n, m) = n^(m-1)*(n+1)^(n-m+1), n >= m >= 1; E.g.f. for column m: A(m, x); A(0, x) = 1/(1+W(-x)); A(1, x) = -1 - (d/dx)W(-x) = -1-W(-x)/((1+W(-x))*x); A(2, x) = A(1, x)-int(A(1, x), x)/x-(1/x+x); recursion: A(m, x) = A(m-1, x)-int(A(m-1, x), x)/x-((m-1)^(m-1))*(x^(m-1))/(m-1)!, m >= 3; W(x) principal branch of Lambert's function. EXAMPLE {1}; {1,2}; {4,9,6}; {27,64,48,36}; ... Fourth row polynomial (n=3): p(3,x) = 27 + 64*x + 48*x^2 + 36*x^3. MATHEMATICA a[n_, m_] /; n < m = 0; a[0, 0] = 1; a[n_, 0] := n^n; a[n_, m_] := n^(m-1)*(n+1)^(n-m+1); Table[a[n, m], {n, 0, 8}, {m, 0, n}] // Flatten (* Jean-François Alcover, Jun 20 2013 *) CROSSREFS Column sequences are A000312(n), n >= 1, A055860 (A000169), A055861 (A053506), A055862-3 for m=0..4, row sums: A045531(n+1)= |A039621(n+1, 2)|, n >= 0. Sequence in context: A304753 A063507 A241473 * A141389 A133757 A076125 Adjacent sequences:  A055855 A055856 A055857 * A055859 A055860 A055861 KEYWORD easy,nonn,tabl AUTHOR Wolfdieter Lang, Jun 20 2000 STATUS approved

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Last modified June 17 22:17 EDT 2019. Contains 324200 sequences. (Running on oeis4.)