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 A233472 Triangle T(n,k) giving denominator of coefficient of x^k in a polynomial p(n) defined as a determinant. 1
 1, 2, 1, 72, 12, 12, 43200, 3600, 1440, 2160, 423360000, 21168000, 4704000, 3024000, 6048000, 67212633600000, 2240421120000, 320060160000, 120022560000, 106686720000, 266716800000, 172153600393420800000, 4098895247462400000 (list; table; graph; refs; listen; history; text; internal format)
 OFFSET 0,2 COMMENTS Numerators are (-1)^k. The polynomials p(n) satisfy the condition integral_{x=0..1} x^k*p(n) dx = 0, 0<=k (p-> seq(1/abs(coeff(p, x, k)), k=0..n))(Determinant(          Matrix(n+1, (i, j)->`if`(i=1, x^(j-1), 1/(i+j-2))))): seq(T(n), n=0..6);  # Alois P. Heinz, Dec 22 2013 MATHEMATICA a[1, k_] := x^(k-1); a[n_, k_] := 1/(n+k-2); p[m_] := Det[Table[a[n, k], {n, 1, m+1}, {k, 1, m+1}]]; t[n_, k_] := Coefficient[p[n], x, k]; Table[t[n, k] // Denominator, {n, 0, 6}, {k, 0, n}] // Flatten CROSSREFS Sequence in context: A309207 A104024 A339144 * A284596 A216485 A096681 Adjacent sequences:  A233469 A233470 A233471 * A233473 A233474 A233475 KEYWORD nonn,frac,tabl,look AUTHOR Jean-François Alcover, Dec 11 2013 STATUS approved

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Last modified May 26 20:51 EDT 2022. Contains 354092 sequences. (Running on oeis4.)