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

0,2

Links

G. C. Greubel, Table of n, a(n) for n = 0..1000

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

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 *)

Prog

(Magma) [(5*n+1)*Binomial(4*n, n)/(3*n+1) : n in [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

Crossrefs

Cf. A002293, A051945.

Sequence in context: A108452 A363104 A005591 * A147688 A090442 A286867

Adjacent sequences: A052201 A052202 A052203 * A052205 A052206 A052207

Keyword

easy,nonn

Author

Barry E. Williams, Jan 28 2000

Extensions

More terms from James A. Sellers, Jan 31 2000

Status

approved