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A000763
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Number of interval orders constructed from n intervals of generic lengths.
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1
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1, 3, 19, 195, 2831, 53703, 1264467, 35661979, 1173865927, 44218244943, 1877050837355, 88693432799667, 4618194424504623, 262771389992099719, 16223185411792992403, 1080238361814167993739, 77171781603974127429527
(list; graph; refs; listen; history; internal format)
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OFFSET
| 1,2
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FORMULA
| E.g.f. E(x) satisfies E'/E = y^2, where y=1+x+5*x^2/2+... is defined by y(2-exp(xy))=1.
E.g.f.: exp(int(RootOf(2*_Z-_Z*exp(x*_Z)-1)^2, x)).
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MATHEMATICA
| max = 17; e[x_] := Sum[c[k]*x^k, {k, 0, max}]; c[0] = 1; c[1] = 1; y[x_] := Sum[d[k]*x^k, {k, 0, max}]; d[0] = 1; d[1] = 1; cc = CoefficientList[ Series[ e'[x]/e[x] - y[x]^2, {x, 0, max}], x]; dd = CoefficientList[ Series[ y[x]*(2 - Exp[x*y[x]]) - 1, {x, 0, max}], x]; eqdd = Thread[dd == 0]; soldd = Solve[ Thread[dd == 0] ]; eqcc = Thread[(cc /. soldd[[1]]) == 0]; solcc = Solve[ Most[eqcc] ] ; A000763 = (Table[c[k], {k, 1, max}] /. solcc[[1]])*Range[max]! (* From Jean-François Alcover, Jan 13 2012, after e.g.f. *)
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CROSSREFS
| Cf. A052894.
Sequence in context: A053554 A048172 A079145 * A001832 A195511 A123681
Adjacent sequences: A000760 A000761 A000762 * A000764 A000765 A000766
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KEYWORD
| nonn,nice,easy
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AUTHOR
| R. P. Stanley [ rstan(AT)math.mit.edu ]
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EXTENSIONS
| More terms from Vladeta Jovovic (vladeta(AT)eunet.rs), Nov 04 2001
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