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Search: id:A053979
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| A053979 |
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Triangle T(n,k) giving number of rooted maps regardless of genus with n edges and k nodes (n >= 0, k=1..n+1). |
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+0
3
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| 1, 1, 1, 3, 5, 2, 15, 32, 22, 5, 105, 260, 234, 93, 14, 945, 2589, 2750, 1450, 386, 42, 10395, 30669, 36500, 22950, 8178, 1586, 132, 135135, 422232, 546476, 388136, 166110, 43400, 6476, 429, 2027025, 6633360, 9163236, 7123780, 3463634, 1092560
(list; table; graph; listen)
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OFFSET
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0,4
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REFERENCES
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D. Arques and J.-F. Beraud, Rooted maps on orientable surfaces..., Discrete Math., 215 (2000), 1-12.
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FORMULA
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G.f.=t/(1-(t+1)z/(1-(t+2)z/(1-(t+3)z/(1-(t+4)z/(1-(t+5)z/(1-... (Eq. (5) in the Arques-Beraud reference). - Emeric Deutsch (deutsch(AT)duke.poly.edu), Apr 01 2005
Sum_{k, 0<=k<=n}(-1)^k*2^(n-k)*T(n,k)=A128709(n). Sum_{k, 0<=k<=n}T(n,k)=A00698(n+1). - Philippe DELEHAM (kolotoko(AT)wanadoo.fr), Mar 24 2007
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EXAMPLE
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1; 1,1; 3,5,2; 15,32,22,5; 105,260,234,93,14; ...
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MAPLE
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G:=t/(1-(t+1)*z/(1-(t+2)*z/(1-(t+3)*z/(1-(t+4)*z/(1-(t+5)*z/(1-(t+6)*z/(1-(t+7)*z/(1-(t+8)*z/(1-(t+9)*z/(1-(t+10)*z/(1-(t+11)*z/(1-(t+12)*z)))))))))))):Gser:=simplify(series(G, z=0, 10)):P[0]:=t:for n from 1 to 9 do P[n]:=sort(expand(coeff(Gser, z^n))) od:seq(seq(coeff(P[n], t^k), k=1..n+1), n=0..9); (Deutsch)
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CROSSREFS
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Sequence in context: A102507 A076556 A108426 this_sequence A130847 A010615 A114865
Adjacent sequences: A053976 A053977 A053978 this_sequence A053980 A053981 A053982
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KEYWORD
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nonn,tabl,easy
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AUTHOR
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njas, Apr 09 2000
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EXTENSIONS
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More terms from Emeric Deutsch (deutsch(AT)duke.poly.edu), Apr 01 2005
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