OFFSET
1,1
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 and A. B. Lehman, Counting rooted maps by genus. III: Nonseparable maps, J. Combinatorial Theory Ser. B, Vol. 18, No. 3 (1975), pp. 222-259. See Table IVa.
Index entries for linear recurrences with constant coefficients, signature (6,-15,20,-15,6,-1).
FORMULA
G.f.: x*(3+2*x)/(1-x)^6.
a(n) = n*(n+1)*(n+2)^2*(n+3)/24. - Bruno Berselli, May 17 2011
a(n) = A027777(n)/2. - Zerinvary Lajos, Mar 23 2007
a(n) = binomial(n+2,n)*binomial(n+2,n-1) - binomial(n+2,n+1)*binomial(n+2,n-2). - J. M. Bergot, Apr 07 2013
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). - Harvey P. Dale, Dec 24 2013
Sum_{n>=1} 1/a(n) = 2*Pi^2 - 58/3. - Jaume Oliver Lafont, Jul 15 2017
Sum_{n>=1} (-1)^(n+1)/a(n) = Pi^2 + 16*log(2) - 62/3. - Amiram Eldar, Jan 28 2022
MAPLE
MATHEMATICA
CoefficientList[Series[x (3+2x)/(1-x)^6, {x, 0, 40}], x] (* or *) LinearRecurrence[ {6, -15, 20, -15, 6, -1}, {0, 3, 20, 75, 210, 490}, 40] (* Harvey P. Dale, Dec 24 2013 *)
PROG
(Magma) [n*(n+1)*(n+2)^2*(n+3)/24: n in [1..50]]; // Vincenzo Librandi, May 19 2011
CROSSREFS
KEYWORD
nonn,easy,nice
AUTHOR
EXTENSIONS
G.f. adapted to the offset by Bruno Berselli, May 17 2011
STATUS
approved