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Search: id:A060226
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| 1, 0, 2, 15, 148, 1845, 27906, 496951, 10188872, 236425545, 6125795110, 175311670611, 5492360400924, 186965800764925, 6871755333266474, 271213787997489135, 11440441827615801616, 513645612633274386705
(list; graph; listen)
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OFFSET
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0,3
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COMMENT
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For n>0, a(n)= number of endofunctions of [n] mapping some x<>1 to 1. - Len Smiley (smiley(AT)math.uaa.alaska.edu), Nov 15 2001 (Endofunction interpretation from a(n)=n*[n^(n-1)-(n-1)^(n-1)].)
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REFERENCES
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Problem 10781, Amer. Math. Monthly, 107, Feb. 2000, p. 176
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LINKS
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D. Callan, A Bijection between Marked Trees
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FORMULA
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a(n) = n*A055869(n-1). As n increases, a(n)/a(n-1)-a(n-1)/a(n-2) tends towards e.
E.g.f.: (1-x)/(1-T), where T=T(x) is Euler's tree function (see A000169). The E.g.f. for n>0 terms only (applicable to endofunctions) is (T - x)/(1 - T). - Len Smiley (smiley(AT)math.uaa.alaska.edu), Dec 10 2001
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MAPLE
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f := n->n*sum(binomial(n-1, j-1)*(n-1)^(n-j), j=2..n); g := n->n^n-n*(n-1)^(n-1); h := n->sum( binomial(n, j)*j^(j-1)*(n-j)^(n-j), j=2..n); k := n->sum(binomial(n, j-1)*(j-1)^(j-1)*(n-j)^(n-j), j=2..n); #t hen a(n)=f(n)=g(n)=k(n)
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CROSSREFS
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Cf. A000312 A045531 A055869.
Sequence in context: A005415 A111686 A001854 this_sequence A002103 A124548 A139085
Adjacent sequences: A060223 A060224 A060225 this_sequence A060227 A060228 A060229
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KEYWORD
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nonn
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AUTHOR
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Henry Bottomley (se16(AT)btinternet.com), Jul 12 2001
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