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A113236
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Number of partitions of {1,..,n} into any number of lists of size not equal to 3, where a list means an ordered subset, cf. A000262.
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2
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1, 1, 3, 7, 49, 321, 2851, 24823, 256257, 2887489, 36759331, 507010791, 7597222513, 122184356737, 2106356007939, 38693238713431, 754792977928321, 15572911248409473, 338800604611562947
(list; graph; refs; listen; history; internal format)
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OFFSET
| 0,3
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FORMULA
| E.g.f.: exp(x*(1-x^2+x^3)/(1-x)) Expression as a sum involving generalized Laguerre polynomials, in Mathematica notation: a(n)=n!*Sum[(-1)^k*LaguerreL[n - 3*k, -1, -1]/k!, {k, 0, Floor[n/3]}], n=0, 1....
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MATHEMATICA
| Range[0, 18]!*CoefficientList[ Series[ Exp[x*(1-x^2+x^3)/(1 - x)], {x, 0, 18}], x] - Zerinvary Lajos (zerinvarylajos(AT)yahoo.com), Mar 23 2007
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CROSSREFS
| Cf. A052845, A113235.
Sequence in context: A190444 A118393 A113775 * A035499 A120788 A041277
Adjacent sequences: A113233 A113234 A113235 * A113237 A113238 A113239
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KEYWORD
| nonn
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AUTHOR
| Karol A. Penson (penson(AT)lptl.jussieu.fr), Oct 19 2005
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