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 A053383 Triangle T(n,k) giving denominator of coefficient of x^(n-k) in Bernoulli polynomial B(n, x), n >= 0, 0<=k<=n. 23
 1, 1, 2, 1, 1, 6, 1, 2, 2, 1, 1, 1, 1, 1, 30, 1, 2, 3, 1, 6, 1, 1, 1, 2, 1, 2, 1, 42, 1, 2, 2, 1, 6, 1, 6, 1, 1, 1, 3, 1, 3, 1, 3, 1, 30, 1, 2, 1, 1, 5, 1, 1, 1, 10, 1, 1, 1, 2, 1, 1, 1, 1, 1, 2, 1, 66, 1, 2, 6, 1, 1, 1, 1, 1, 2, 1, 6, 1, 1, 1, 1, 1, 2, 1, 1, 1, 2, 1, 1, 1, 2730, 1, 2, 1, 1, 6, 1, 7, 1, 10 (list; table; graph; refs; listen; history; text; internal format)
 OFFSET 0,3 REFERENCES M. Abramowitz and I. A. Stegun, eds., Handbook of Mathematical Functions, National Bureau of Standards Applied Math. Series 55, 1964 (and various reprintings), p. 809. L. Comtet, Advanced Combinatorics, Reidel, 1974, p. 48, [14a]. M. Kauers and P. Paule, The Concrete Tetrahedron, Springer 2011, p. 53. H. Rademacher, Topics in Analytic Number Theory, Springer, 1973, Chap. 1. LINKS T. D. Noe, Rows n=0..50 of triangle, flattened M. Abramowitz and I. A. Stegun, eds., Handbook of Mathematical Functions, National Bureau of Standards, Applied Math. Series 55, Tenth Printing, 1972 [alternative scanned copy]. D. H. Lehmer, A new approach to Bernoulli polynomials, The American mathematical monthly 95.10 (1988): 905-911. EXAMPLE The polynomials B(0,x), B(1,x), B(2,x), ... are 1; x-1/2; x^2-x+1/6; x^3-3/2*x^2+1/2*x; x^4-2*x^3+x^2-1/30; x^5-5/2*x^4+5/3*x^3-1/6*x; x^6-3*x^5+5/2*x^4-1/2*x^2+1/42; ... Triangle A053382/A053383 begins: 1, 1, -1/2, 1, -1, 1/6, 1, -3/2, 1/2, 0, 1, -2, 1, 0, -1/30, 1, -5/2, 5/3, 0, -1/6, 0, 1, -3, 5/2, 0, -1/2, 0, 1/42, ... Triangle A196838/A196839 begins (this is the reflected version): 1, -1/2, 1, 1/6, -1, 1, 0, 1/2, -3/2, 1, -1/30, 0, 1, -2, 1, 0, -1/6, 0, 5/3, -5/2, 1, 1/42, 0, -1/2, 0, 5/2, -3, 1, ... MAPLE with(numtheory); bernoulli(n, x); MATHEMATICA t[n_, k_] := Denominator[ Coefficient[ BernoulliB[n, x], x, n - k]]; Flatten[ Table[t[n, k], {n, 0, 13}, {k, 0, n}]] (* Jean-François Alcover, Jan 15 2013 *) PROG (PARI) v=[]; for(n=0, 6, v=concat(v, apply(denominator, Vec(bernpol(n))))); v \\ Charles R Greathouse IV, Jun 08 2012 CROSSREFS Three versions of coefficients of Bernoulli polynomials: A053382/A053383; for reflected version see A196838/A196839; see also A048998 and A048999. Cf. A144845 (lcm of row n) Sequence in context: A152656 A096162 A306297 * A181538 A322128 A125731 Adjacent sequences:  A053380 A053381 A053382 * A053384 A053385 A053386 KEYWORD nonn,easy,nice,frac,tabl AUTHOR N. J. A. Sloane, Jan 06 2000 EXTENSIONS More terms from James A. Sellers, Jan 10 2000 STATUS approved

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Last modified February 26 12:43 EST 2020. Contains 332280 sequences. (Running on oeis4.)