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 A033842 Triangle of coefficients of certain polynomials (exponents in decreasing order). 12
 1, 1, 1, 3, 3, 1, 16, 16, 6, 1, 125, 125, 50, 10, 1, 1296, 1296, 540, 120, 15, 1, 16807, 16807, 7203, 1715, 245, 21, 1, 262144, 262144, 114688, 28672, 4480, 448, 28, 1, 4782969, 4782969, 2125764, 551124, 91854, 10206, 756, 36, 1, 100000000 (list; table; graph; refs; listen; history; text; internal format)
 OFFSET 0,4 COMMENTS See A049323. LINKS Table of n, a(n) for n=0..45. W. Lang, On generalizations of Stirling number triangles, J. Integer Seqs., Vol. 3 (2000), #00.2.4. Thierry Lévy, The Number of Prefixes of Minimal Factorisations of a Cycle, The Electronic Journal of Combinatorics, 23(3) (2016), #P3.35 FORMULA a(n, m) = binomial(n+1, m)*(n+1)^(n-m-1), n >= m >= 0 else 0. EXAMPLE {1}; {1,1}; {3,3,1}; {16,16,6,1}; {125,125,50,10,1}; .... E.g. third row {3,3,1} corresponds to polynomial p(2,x)= 3*x^2+3*x+1. CROSSREFS a(n, 0)= A000272(n+1), n >= 0 (first column), a(n, 1)= A000272(n+1), n >= 1 (second column). p(k-1, -x)/(1-k*x)^k = (-1+1/(1-k*x)^k)/(x*k^2) is for k=1..5 G.f. for A000012, A001792, A036068, A036070, A036083, respectively. See also A049323. Sequence in context: A105599 A239895 A106210 * A104417 A121438 A108391 Adjacent sequences: A033839 A033840 A033841 * A033843 A033844 A033845 KEYWORD easy,nonn,tabl AUTHOR Wolfdieter Lang STATUS approved

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Last modified August 4 01:12 EDT 2024. Contains 374905 sequences. (Running on oeis4.)