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A006413
Number of nonseparable tree-rooted planar maps with n + 4 edges and 5 vertices.
(Formerly M4031)
4
5, 210, 3150, 27556, 170793, 829920, 3359356, 11786190, 36845718, 104719524, 274707420, 672982128, 1554007910, 3407724936, 7139933088, 14366348780, 27878652291, 52364814150, 95497666810, 169546939380, 293722986375, 497527759560, 825473130300, 1343631834090
OFFSET
1,1
REFERENCES
N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, Academic Press, 1995 (includes this sequence).
T. R. S. Walsh and A. B. Lehman, Counting rooted maps by genus. III: Nonseparable maps, J. Combinatorial Theory Ser. B 18 (1975), 222-259.
FORMULA
a(n) = 5 * binomial(n + 6, 7) + 170 * binomial(n + 6, 8) + 1440 * binomial(n + 6, 9) + 4906 * binomial(n + 6, 10) + 7927 * binomial(n + 6, 11) + 6090 * binomial(n + 6, 12) + 1794 * binomial(n + 6, 13). - Sean A. Irvine, Apr 03 2017
a(n) = binomial(n+7,8)*(n + 4)*(23*n^4 + 279*n^3 + 941*n^2 + 599*n + 138)/1980. - Andrew Howroyd, Apr 05 2021
PROG
(PARI) a(n) = {binomial(n+7, 8)*(n + 4)*(23*n^4 + 279*n^3 + 941*n^2 + 599*n + 138)/1980} \\ Andrew Howroyd, Apr 05 2021
CROSSREFS
Column 5 of A342984.
Sequence in context: A068531 A144139 A020541 * A055316 A203470 A165208
KEYWORD
nonn
AUTHOR
EXTENSIONS
Terms a(10) and beyond from Andrew Howroyd, Apr 05 2021
STATUS
approved

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Last modified September 20 15:18 EDT 2024. Contains 376072 sequences. (Running on oeis4.)