OFFSET
0,2
REFERENCES
J. M. Borwein and P. B. Borwein, Pi and the AGM, Wiley, 1987, p. 386.
LINKS
G. C. Greubel, Table of n, a(n) for n = 0..1000
FORMULA
Sum_{n>=1} 1/a(n) = 17*Pi^4/3240. (Comtet, 1974)
a(n) = a(n-1)*(4*n-2)*n^3/(n-1)^4, n>1. - Michael Somos, Apr 18 2003
Equals A002736*n^2. - Zerinvary Lajos, May 28 2006
From Ilya Gutkovskiy, Feb 07 2017: (Start)
G.f.: 2*x*(1 + 30*x + 72*x^2 + 8*x^3)/(1 - 4*x)^(9/2).
a(n) ~ 4^n*n^(7/2)/sqrt(Pi). (End)
MAPLE
with(combinat):for n from 0 to 18 do printf(`%d, `, n^3*sum(binomial(2*n, n), k=1..n)) od: # Zerinvary Lajos, Mar 13 2007
MATHEMATICA
Table[n^4*Binomial[2 n, n], {n, 0, 18}] (* or *)
CoefficientList[Series[2 x (1 + 30 x + 72 x^2 + 8 x^3)/(1 - 4 x)^(9/2), {x, 0, 18}], x] (* Michael De Vlieger, Feb 07 2017 *)
PROG
(PARI) a(n)=if(n<1, 0, n^4*binomial(2*n, n))
CROSSREFS
KEYWORD
easy,nonn
AUTHOR
Benoit Cloitre, Apr 07 2002
STATUS
approved