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A006468
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Number of rooted planar maps with 4 faces and n vertices and no isthmuses.
(Formerly M3984)
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3
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5, 37, 150, 449, 1113, 2422, 4788, 8790, 15213, 25091, 39754, 60879, 90545, 131292, 186184, 258876, 353685, 475665, 630686, 825517, 1067913, 1366706, 1731900, 2174770, 2707965, 3345615, 4103442, 4998875, 6051169, 7281528, 8713232, 10371768, 12284965, 14483133, 16999206
(list;
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refs;
listen;
history;
text;
internal format)
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OFFSET
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1,1
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REFERENCES
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N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, Academic Press, 1995 (includes this sequence).
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LINKS
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FORMULA
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G.f.: -x*(x^3-4*x^2+2*x+5)/(x-1)^7, equivalent to a(n) = n *(n+1) *(n+2) *(2*n^3 +33*n^2 +142*n +123) /360, conjectured in Simon Plouffe's Master's thesis, 1992.
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PROG
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(PARI) a(n) = {n *(n+1) *(n+2) *(2*n^3 + 33*n^2 + 142*n + 123) /360} \\ Andrew Howroyd, Apr 02 2021
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CROSSREFS
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KEYWORD
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nonn
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AUTHOR
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EXTENSIONS
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STATUS
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approved
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