OFFSET
0,2
COMMENTS
Even-indexed members of tenth column of Pascal's triangle A007318.
Number of standard tableaux of shape (2n+1,1^9). - Emeric Deutsch, May 30 2004
LINKS
Vincenzo Librandi, Table of n, a(n) for n = 0..200
Milan Janjić, Two Enumerative Functions.
Index entries for linear recurrences with constant coefficients, signature (10,-45,120,-210,252,-210,120,-45, 10,-1).
FORMULA
a(n) = binomial(2*n+9, 9) = A000582(2*n+9).
G.f.: (1 + 45*x + 210*x^2 + 210*x^3 + 45*x^4 + x^5) / (1-x)^10.
G.f.: (1 + x) * (x^4 + 44*x^3 + 166*x^2 + 44*x + 1) / (1-x)^10.
a(n) = 10*a(n-1) - 45*a(n-2) + 120*a(n-3) - 210*a(n-4) + 252*a(n-5) - 210*a(n-6) + 120*a(n-7) - 45*a(n-8) + 10*a(n-9) - a(n-10) for n > 9. - Wesley Ivan Hurt, Dec 05 2016
From Amiram Eldar, Nov 03 2022: (Start)
Sum_{n>=0} 1/a(n) = 1152*log(2) - 27912/35.
Sum_{n>=0} (-1)^n/a(n) = 36*Pi - 3924/35. (End)
MAPLE
MATHEMATICA
Table[Binomial[2n+9, 9], {n, 0, 30}] (* Harvey P. Dale, Dec 08 2011 *)
PROG
(Magma) [Binomial(2*n+9, 9): n in [0..30]]; // Vincenzo Librandi, Oct 07 2011
(PARI) for(n=0, 30, print1(binomial(2*n+9, 9), ", ")) \\ G. C. Greubel, Sep 03 2018
CROSSREFS
KEYWORD
nonn,easy
AUTHOR
STATUS
approved