A052204 a(n) = (5n+1)*C(4n,n)/(3n+1).
1, 6, 44, 352, 2940, 25194, 219604, 1937520, 17250012, 154663960, 1394538288, 12631852688, 114858935204, 1047772373340, 9584557428600, 87885886492320, 807564936805020, 7434289153896264, 68551275793965328, 633038816547052800
Offset: 0
Links
- G. C. Greubel, Table of n, a(n) for n = 0..1000
Programs
-
Magma
[(5*n+1)*Binomial(4*n,n)/(3*n+1) : n in [0..20]]; // Wesley Ivan Hurt, Aug 10 2016
-
Maple
A052204:=n->(5*n+1)*binomial(4*n,n)/(3*n+1): seq(A052204(n), n=0..20); # Wesley Ivan Hurt, Aug 10 2016
-
Mathematica
Table[(5 n + 1) Binomial[4 n, n]/(3 n + 1), {n, 0, 20}] (* Wesley Ivan Hurt, Aug 10 2016 *) -
PARI
for(n=0,25, print1((5*n+1)*binomial(4*n,n)/(3*n+1), ", ")) \\ G. C. Greubel, Feb 16 2017
Formula
G.f.: (2*g-1)*g/(4-3*g) where g = 1+x*g^4 is the g.f. of A002293. - Mark van Hoeij, Nov 11 2011
Conjecture: 6*n*(3*n-1)*(3*n+1)*a(n) + (-809*n^3 + 1444*n^2 - 1505*n + 582)*a(n-1) + 88*(4*n-5)*(4*n-7)*(2*n-3)*a(n-2) = 0. - R. J. Mathar, Sep 29 2012
a(n) ~ 5*2^(8*n+1/2)*3^(-3*n-3/2)/sqrt(Pi*n). - Ilya Gutkovskiy, Aug 10 2016
Extensions
More terms from James Sellers, Jan 31 2000