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A088957
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Hyperbinomial transform of the sequence of 1's.
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6
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1, 2, 6, 29, 212, 2117, 26830, 412015, 7433032, 154076201, 3608522954, 94238893883, 2715385121740, 85574061070045, 2928110179818478, 108110945014584623, 4284188833355367440, 181370804507130015569
(list; graph; refs; listen; history; internal format)
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OFFSET
| 0,2
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COMMENTS
| See A088956 for the definition of the hyperbinomial transform.
a(n) is the number of partial functions on {1,2,...,n} that are endofunctions with no cycles of length > 1. The triangle A088956 classifies these functions according to the number of undefined elements in the domain. The triangle A144289 classifies these functions according to the number of edges in their digraph representation (considering the empty function to have 1 edge). The triangle A203092 classifies these functions according to the number of connected components. - Geoffrey Critzer Dec 29 2011.
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FORMULA
| a(n) = sum(k=0, n, (n-k+1)^(n-k-1)*C(n, k)). E.g.f. A(x) = exp(x+sum(n>=1, n^(n-1)*x^n/n!)).
E.g.f.: -LambertW(-x)*exp(x)/x. - Vladeta Jovovic (vladeta(AT)eunet.rs), Oct 27 2003
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EXAMPLE
| a(5) = 1296+625+160+30+5+1 = sum of row 5 of triangle A088956.
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MATHEMATICA
| nn = 16; t = Sum[n^(n - 1) x^n/n!, {n, 1, nn}];
Range[0, nn]! CoefficientList[Series[Exp[x] Exp[t], {x, 0, nn}], x] (*Geoffrey Critzer, Dec 29 2011*)
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CROSSREFS
| Cf. A088956 (triangle).
Row sums of A144289. [From Alois P. Heinz (heinz(AT)hs-heilbronn.de), Jun 01 2009]
Cf. A086331,A000169
Sequence in context: A020126 A124529 A187006 * A030538 A181812 A076978
Adjacent sequences: A088954 A088955 A088956 * A088958 A088959 A088960
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KEYWORD
| nonn
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AUTHOR
| Paul D. Hanna (pauldhanna(AT)juno.com), Oct 26 2003
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