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A006470 Number of rooted planar maps.
(Formerly M2075)
3
2, 15, 60, 175, 420, 882, 1680, 2970, 4950, 7865, 12012, 17745, 25480, 35700, 48960, 65892, 87210, 113715, 146300, 185955, 233772, 290950, 358800, 438750, 532350, 641277, 767340, 912485, 1078800, 1268520, 1484032, 1727880, 2002770, 2311575, 2657340, 3043287, 3472820, 3949530, 4477200, 5059810, 5701542, 6406785, 7180140 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,1

COMMENTS

a(n) is the number of ordered rooted trees with n+3 non-root nodes that have 3 leaves; see A108838. - Joerg Arndt, Aug 18 2014

REFERENCES

N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, Academic Press, 1995 (includes this sequence).

LINKS

Vincenzo Librandi, Table of n, a(n) for n = 1..1000

T. R. S. Walsh, A. B. Lehman, Counting rooted maps by genus. III: Nonseparable maps, J. Combinatorial Theory Ser. B 18 (1975), 222-259.

Index entries for linear recurrences with constant coefficients, signature (6,-15,20,-15,6,-1).

FORMULA

a(n) = (n+1)*binomial(n+3, 4).

a(n) = C(n+2, 2)*C(n+4, 3)/2; G.f.: x*(2+3*x)/(1-x)^6. - Zerinvary Lajos, Dec 14 2005

From Wesley Ivan Hurt, May 02 2015: (Start)

a(n) = 6*a(n-1)-15*a(n-2)+20*a(n-3)-15*a(n-4)+6*a(n-5)-a(n-6).

a(n) = n*(n+1)^2*(n+2)*(n+3)/24. (End)

Sum_{n>=1} 1/a(n) = 61/3 - 2*Pi^2. - Jaume Oliver Lafont, Jul 15 2017

MAPLE

A006470:=n->(n+1)*binomial(n+3, 4): seq(A006470(n), n=1..50); # Wesley Ivan Hurt, May 02 2015

MATHEMATICA

Table[n (n + 1)^2 (n + 2) (n + 3) / 24, {n, 50}] (* Vincenzo Librandi, May 03 2015 *)

PROG

(MAGMA) [(n+1)*Binomial(n+3, 4): n in [1..30]]; // Vincenzo Librandi, Jun 09 2013

CROSSREFS

Cf. A027789/2.

Sequence in context: A295828 A126019 A071237 * A084169 A000181 A047146

Adjacent sequences:  A006467 A006468 A006469 * A006471 A006472 A006473

KEYWORD

nonn,easy

AUTHOR

N. J. A. Sloane

EXTENSIONS

Typo in Mma program corrected by Vincenzo Librandi, Jun 09 2013

STATUS

approved

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Last modified December 13 00:17 EST 2017. Contains 295954 sequences.