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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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0
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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
(list; graph; refs; listen; history; internal format)
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OFFSET
| 0,3
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REFERENCES
| F. Bergeron, M. Bousquet-M\'{e}lou and S. Dulucq, Standard paths in the composition poset, Ann. Sci. Math. Quebec, 19 (1995), no. 2, 139-151.
N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, Academic Press, 1995 (includes this sequence).
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LINKS
| F. Bergeron, M. Bousquet-M\'{e}lou and S. Dulucq, Standard paths in the composition poset
Index entries for sequences related to posets
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FORMULA
| 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).
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PROG
| (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
| Sequence in context: A200403 A113226 A071075 * A101053 A155857 A071076
Adjacent sequences: A007552 A007553 A007554 * A007556 A007557 A007558
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KEYWORD
| nonn
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AUTHOR
| Simon Plouffe (simon.plouffe(AT)gmail.com)
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