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A006471
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Number of tree-rooted planar maps with 4 faces and n vertices and no isthmuses.
(Formerly M4021)
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2
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5, 84, 650, 3324, 13020, 42240, 118998, 300300, 693693, 1490060, 3011580, 5779592, 10608000, 18728832, 31957620, 52907400, 85261341, 134115300, 206402966, 311417700, 461446700, 672534720, 965396250, 1366496820, 1909325925, 2635885980, 3598423704, 4861432400, 6503955744, 8622225920
(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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a(n) = (n*(2+n)^2*(3240 + 10158*n + 11777*n^2 + 6400*n^3 + 1770*n^4 + 242*n^5 + 13*n^6))/60480.
G.f.: x*(4*x^3 + 35*x^2 + 34*x + 5) / (x-1)^10. (End)
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PROG
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(PARI) a(n) = (n*(2+n)^2*(3240 +10158*n +11777*n^2 +6400*n^3 +1770*n^4 +242*n^5 +13*n^6))/60480 \\ Andrew Howroyd, Apr 03 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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Name clarified and terms a(12) and beyond from Andrew Howroyd, Apr 03 2021
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STATUS
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approved
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