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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 A296661 A000181 Adjacent sequences:  A006467 A006468 A006469 * A006471 A006472 A006473 KEYWORD nonn,easy AUTHOR STATUS approved

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Last modified January 23 17:13 EST 2019. Contains 319399 sequences. (Running on oeis4.)