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A007555
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Number of standard paths of length n in composition poset.
(Formerly M1667)
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1
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1, 1, 2, 6, 23, 107, 586, 3690, 26245, 207997, 1817090, 17345358, 179595995, 2004596903, 23992185226, 306497734962, 4162467826729, 59882101858777, 909688617178178, 14551535460258966, 244477068964113407
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OFFSET
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0,3
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REFERENCES
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N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, Academic Press, 1995 (includes this sequence).
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LINKS
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FORMULA
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E.g.f.: exp(-x)/(cosh(x/sqrt(2)) - sqrt(2)*sinh(x/sqrt(2)))^2.
a(n) is asymptotic to n!(c1(n+1+c2)+c2)/((sqrt(2)c2)^n*c1^c1*c2^2) where c1=1+sqrt(2), c2=log(c1).
G.f.: 1/Q(0), where Q(k) = 1 - x*(2*k+1) - x^2*(k+1)*(k+2)/2/Q(k+1) ; (continued fraction). - Sergei N. Gladkovskii, Sep 29 2013
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MATHEMATICA
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terms = 21;
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PROG
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(PARI) a(n)=local(X, w); if(n<0, 0, X=x+x*O(x^n); w=quadgen(8); n!*polcoeff(exp(-X)/(cosh(X/w)-w*sinh(X/w))^2, n))
(PARI) a(n)=if(n<0, 0, n!*polcoeff(exp(intformal(1/(1-intformal(1/cosh((x+x*O(x^n))/quadgen(8))^2)))), n))
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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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