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Search: id:A002802
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| A002802 |
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(2*n+3)!/(6*n!*(n+1)!).
(Formerly M4724 N2019)
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+0
16
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| 1, 10, 70, 420, 2310, 12012, 60060, 291720, 1385670, 6466460, 29745716, 135207800, 608435100, 2714556600, 12021607800, 52895074320, 231415950150, 1007340018300, 4365140079300, 18839025605400, 81007810103220, 347176329013800, 1483389769422600
(list; graph; listen)
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OFFSET
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0,2
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COMMENT
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For n >= 1 a(n) is also the number of rooted bicolored unicelluar maps of genus 1 on n+2 edges. - Ahmed Fares (ahmedfares(AT)my-deja.com), Aug 20 2001
a(n)=A051133(n+1)/3 =A000911(n)/6. - Zerinvary Lajos (zerinvarylajos(AT)yahoo.com), Jun 02 2007
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REFERENCES
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Alain Goupil and Gilles Schaeffer, Factoring N-Cycles and Counting Maps of Given Genus . Europ. J. Combinatorics (1998) 19 819-834.
C. Jordan, Calculus of Finite Differences. Budapest, 1939, p. 449.
T. R. S. Walsh and A. B. Lehman, Counting rooted maps by genus. I, J. Comb. Theory, B, 13, No.3 (1972), 192-218 (Tab.1).
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FORMULA
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G.f.: (1 - 4*x)^(-5/2).
Asymptotic expression for a(n) is a(n) ~ (n+2)^(3/2) * 4^(n+2) / (sqrt(Pi) * 48)
a(n) = Sum (a+b+c+d+e=n, f(a)*f(b)*f(c)*f(d)*f(e)) with f(n)=binomial(2n, n)=A000984(n). - DELEHAM Philippe (kolotoko(AT)wanadoo.fr), Jan 22 2004
a(n-1)=1/4*sum(k=1, n, k*(k+1)*binomial(2*k, k)) - Benoit Cloitre (benoit7848c(AT)orange.fr), Mar 20 2004
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MAPLE
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with(combinat):for n from 2 to 24 do printf(`%d, `, n*sum(binomial(2*n, n)/12, k=2..n)) od: - Zerinvary Lajos (zerinvarylajos(AT)yahoo.com), Mar 13 2007
with(combinat):a:=n->sum(sum(numbcomp(2*n, n)/6, j=2..n), k=1..n): seq(a(n), n=2..24); - Zerinvary Lajos (zerinvarylajos(AT)yahoo.com), Jun 02 2007
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CROSSREFS
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Cf. A035309, A000108 (for genus 0 maps).
Adjacent sequences: A002799 A002800 A002801 this_sequence A002803 A002804 A002805
Sequence in context: A025221 A005567 A073391 this_sequence A101029 A122892 A125347
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KEYWORD
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nonn,easy
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AUTHOR
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njas
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