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A006412
Number of nonseparable tree-rooted planar maps with n + 3 edges and 4 vertices.
(Formerly M3697)
4
4, 75, 604, 3150, 12480, 40788, 115500, 292578, 677820, 1459315, 2954952, 5679700, 10438272, 18449760, 31511880, 52213596, 84206100, 132543411, 204105220, 308116050, 456776320, 666022500, 956435220, 1354315950, 1892954700, 2614113099, 3569749200, 4824012424
OFFSET
1,1
REFERENCES
N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, Academic Press, 1995 (includes this sequence).
LINKS
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) = 4 * binomial(n + 4, 5) + 51 * binomial(n + 4, 6) + 163 * binomial(n + 4, 7) + 194 * binomial(n + 4, 8) + 78 * binomial(n + 4, 9). - Sean A. Irvine, Apr 03 2017
a(n) = binomial(n+5,6)*(n + 3)*(13*n^2 + 57*n + 14)/84. - Andrew Howroyd, Apr 05 2021
PROG
(PARI) a(n) = {binomial(n+5, 6)*(n + 3)*(13*n^2 + 57*n + 14)/84} \\ Andrew Howroyd, Apr 05 2021
CROSSREFS
Column 4 of A342984.
Sequence in context: A280889 A257367 A072373 * A206456 A137220 A006236
KEYWORD
nonn
EXTENSIONS
Terms a(11) and beyond from Andrew Howroyd, Apr 05 2021
STATUS
approved