A006413 Number of nonseparable tree-rooted planar maps with n + 4 edges and 5 vertices. (Formerly M4031)

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).

Links

Andrew Howroyd, Table of n, a(n) for n = 1..1000

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.

Cf. A006411, A006412.

Sequence in context: A068531 A144139 A020541 * A055316 A203470 A165208

Adjacent sequences: A006410 A006411 A006412 * A006414 A006415 A006416

Keyword

nonn

Author

N. J. A. Sloane

Extensions

Terms a(10) and beyond from Andrew Howroyd, Apr 05 2021

Status

approved