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 A001898 Denominators of Bernoulli polynomials B(n)(x). (Formerly M2014 N0749) 7
 1, 2, 12, 8, 240, 96, 4032, 1152, 34560, 7680, 101376, 18432, 50319360, 7741440, 6635520, 884736, 451215360, 53084160, 42361159680, 4459069440, 1471492915200, 140142182400, 1758147379200, 152882380800, 417368899584000, 33389511966720, 15410543984640 (list; graph; refs; listen; history; text; internal format)
 OFFSET 0,2 REFERENCES F. N. David, Probability Theory for Statistical Methods, Cambridge, 1949; see pp. 103-104. [There is an error in the recurrence for B_s^{(r)}.] N. E. Nørlund, Vorlesungen über Differenzenrechnung. Springer-Verlag, Berlin, 1924, p. 459. N. J. A. Sloane, A Handbook of Integer Sequences, Academic Press, 1973 (includes this sequence). N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, Academic Press, 1995 (includes this sequence). LINKS N. E. Nörlund, Vorlesungen über Differenzenrechnung, Springer-Verlag, Berlin, 1924 [Annotated scanned copy of pages 144-151 and 456-463] FORMULA These Bernoulli polynomials B(s) = B(s)(x) are defined by: B(0) = 1; B(s) = (-x/s)*Sum_{t=1..s} (-1)^t*binomial(s, t)*Bernoulli(t)*B(s-t), where Bernoulli(t) are the usual Bernoulli numbers A027641/A027642. Also B(s)(1) = Bernoulli(s). EXAMPLE The Bernoulli polynomials B(0)(x) through B(6)(x) are: 1; -(1/2)*x; (1/12)*(3*x-1)*x; -(1/8)*(x-1)*x^2; (1/240)*(15*x^3-30*x^2+5*x+2)*x; -(1/96)*(x-1)*(3*x^2-7*x-2)*x^2; (1/4032)*(63*x^5-315*x^4+315*x^3+91*x^2-42*x-16)*x. MAPLE B:=bernoulli; b:=proc(s) option remember; local t; global r; if s=0 then RETURN(1); fi; expand((-r/s)*add( (-1)^t*binomial(s, t)*B(t)*b(s-t), t=1..s)); end; [seq(denom(b(n)), n=0..30)]; CROSSREFS Cf. A027641, A027642, A100615, A100616, A100655. Sequence in context: A266511 A014964 A173181 * A268230 A229628 A002209 Adjacent sequences:  A001895 A001896 A001897 * A001899 A001900 A001901 KEYWORD nonn AUTHOR EXTENSIONS Entry revised Dec 03 2004 STATUS approved

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Last modified June 25 11:59 EDT 2019. Contains 324352 sequences. (Running on oeis4.)