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A109570
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E.g.f.: x/(1-sinh(x)).
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0
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0, 1, 2, 6, 28, 160, 1086, 8624, 78296, 799488, 9070810, 113208832, 1541351604, 22734473216, 361121134934, 6145880954880, 111569141960752, 2151953994809344, 43948641637067058, 947412315736506368
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OFFSET
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0,3
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COMMENTS
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"Bernoulli numbers" for x/(1-sinh(x)).
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LINKS
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FORMULA
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E.g.f. x/(1-sinh(x)).
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)
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MAPLE
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G:=x/(1-sinh(x)): Gser:=series(G, x=0, 25): 0, seq(n!*coeff(Gser, x^n), n=1..22);
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MATHEMATICA
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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 *)
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CROSSREFS
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KEYWORD
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nonn
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AUTHOR
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STATUS
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approved
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