OFFSET
3,2
REFERENCES
M. Abramowitz and I. A. Stegun, eds., Handbook of Mathematical Functions, National Bureau of Standards Applied Math. Series 55, 1964 (and various reprintings), p. 828.
LINKS
Michael De Vlieger, Table of n, a(n) for n = 3..1209
M. Abramowitz and I. A. Stegun, eds., Handbook of Mathematical Functions, National Bureau of Standards, Applied Math. Series 55, Tenth Printing, 1972 [alternative scanned copy].
Alin Bostan, Frédéric Chyzak, and Vincent Pilaud, Refined product formulas for Tamari intervals, arXiv:2303.10986 [math.CO], 2023.
Milan Janjic, Two Enumerative Functions
Daniel W. Stasiuk, An Enumeration Problem for Sequences of n-ary Trees Arising from Algebraic Operads, Master's Thesis, University of Saskatchewan-Saskatoon (2018).
FORMULA
a(n) = binomial(3n, n-3), n > 2. - Wesley Ivan Hurt, Feb 04 2014
From Ilya Gutkovskiy, Jan 31 2017: (Start)
E.g.f.: (1/6)*x^3*2F2(10/3,11/3; 5,11/2; 27*x/4).
a(n) ~ 3^(3*n+1/2)/(sqrt(Pi*n)*4^(n+2)). (End)
MAPLE
a:=n->sum(binomial(2*n-2, n+j)*binomial(n-1, n-j+1), j=0..n): seq(a(n), n=4..22); # Zerinvary Lajos, Jan 29 2007
MATHEMATICA
Table[Binomial[3n, n-3], {n, 3, 30}] (* Wesley Ivan Hurt, Feb 04 2014 *)
PROG
(PARI) {a(n) = binomial(3*n, n-3)}; \\ G. C. Greubel, Mar 21 2019
(Magma) [Binomial(3*n, n-3): n in [3..30]]; // G. C. Greubel, Mar 21 2019
(Sage) [binomial(3*n, n-3) for n in (3..30)] # G. C. Greubel, Mar 21 2019
(GAP) List([3..30], n-> Binomial(3*n, n-3)) # G. C. Greubel, Mar 21 2019
CROSSREFS
KEYWORD
nonn,easy
AUTHOR
STATUS
approved