OFFSET
0,3
LINKS
Seiichi Manyama, Table of n, a(n) for n = 0..608
FORMULA
a(n) = Sum_{k=0..n} (-1)^(n-k)*A001764(k)^2.
4*(2*n^2 + 9*n + 10)^2*a(n+2) - (713*n^4 + 4230*n^3 + 9317*n^2 + 9000*n + 3200)*a(n+1) - 9*(9*n^2 + 27*n + 20)^2*a(n) = 0.
a(n) ~ 3^(6*n+7)/(745*Pi*n^3*2^(4*n+4)). - Vaclav Kotesovec, Aug 06 2013
MAPLE
A001764 := proc(n) binomial(3*n, n)/(2*n+1) ; end proc:
MATHEMATICA
Table[Sum[Binomial[3k, k]^2(-1)^(n-k)/(2k+1)^2, {k, 0, n}], {n, 0, 20}]
PROG
(Maxima) makelist(sum(binomial(3*k, k)^2*(-1)^(n-k)/(2k+1)^2, k, 0, n), n, 0, 20);
(Magma) [ &+[(-1)^(n-k)*Binomial(3*k, k)^2/(2*k+1)^2: k in [0..n]]: n in [0..16]]; // Bruno Berselli, Apr 11 2011
CROSSREFS
KEYWORD
nonn,easy
AUTHOR
Emanuele Munarini, Apr 08 2011
STATUS
approved