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 A109570 E.g.f.: x/(1-sinh(x)). 0
 0, 1, 2, 6, 28, 160, 1086, 8624, 78296, 799488, 9070810, 113208832, 1541351604, 22734473216, 361121134934, 6145880954880, 111569141960752, 2151953994809344, 43948641637067058, 947412315736506368 (list; graph; refs; listen; history; text; internal format)
 OFFSET 0,3 COMMENTS "Bernoulli numbers" for x/(1-sinh(x)). LINKS FORMULA E.g.f. x/(1-sinh(x)). From Sergei N. Gladkovskii, May 30 2012: (Start) Let E(x)=x/(1-sinh(x)) be the e.g.f., then E(x)=- 1 + 1/(1-x)+ x^4/((1-x)*((1-x)*G(0) - x^2)) ; G(k)= (2*k+2)*(2*k+3)+x^2-(2*k+2)*(2*k+3)*x^2/G(k+1); (continued fraction, Euler's kind, 1-step). E(x)= -1 + 1/(1-x)+ x^4/((1-x)*((1-x)*G(0) - x^2)) ; G(k)= 8*k+6+x^2/(1 + (2*k+2)*(2*k+3)/G(k+1)); (continued fraction, Euler's 2nd kind, 2-step). E(x)= x/(1 - x*G(0)); G(k)= 1 + x^2/(2*(2*k+1)*(4*k+3) + 2*x^2*(2*k+1)*(4*k+3)/(-x^2 - 4*(k+1)*(4*k+5)/G(k+1))); (continued fraction). (End) a(n) ~ n!/(sqrt(2)*(log(1+sqrt(2)))^n). - Vaclav Kotesovec, Jun 27 2013 MAPLE G:=x/(1-sinh(x)): Gser:=series(G, x=0, 25): 0, seq(n!*coeff(Gser, x^n), n=1..22); MATHEMATICA g[x_] = x/(-1 + Sinh[x]) h[x_, n_] = Dt[g[x], {x, n}] a[x_] = Table[ -h[x, n], {n, 0, 50}]; b = a[0] With[{nn=20}, CoefficientList[Series[x/(1-Sinh[x]), {x, 0, nn}], x] Range[0, nn]!] (* Harvey P. Dale, Jul 02 2017 *) CROSSREFS Sequence in context: A184695 A086633 A201950 * A262002 A245633 A156626 Adjacent sequences:  A109567 A109568 A109569 * A109571 A109572 A109573 KEYWORD nonn AUTHOR Roger L. Bagula, Jun 27 2005 STATUS approved

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Last modified April 22 14:30 EDT 2021. Contains 343177 sequences. (Running on oeis4.)