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Partial sums of A002503.
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%I #6 Nov 21 2013 12:50:02

%S 5,19,46,87,131,196,272,362,471,596,735,887,1042,1211,1397,1586,1789,

%T 1997,2206,2425,2652,2882,3119,3384,3659,3957,4264,4575,4889,5210,

%U 5534,5863,6207,6584,6997,7416,7844,8278,8717,9158,9607,10065,10524,10991

%N Partial sums of A002503.

%C Partial sums of numbers n such that binomial(2n,n) is divisible by (n+1)^2. The subsequence of primes in this partial sum begins: 5, 19, 131, 887, 1789, 1997, 3119, 3659, 4889, 6997. The subsequence of primes in this partial sum begins: 196.

%F a(n) = SUM[i=1..n] A002503(i).

%e a(23) = 5 + 14 + 27 + 41 + 44 + 65 + 76 + 90 + 109 + 125 + 139 + 152 + 155 + 169 + 186 + 189 + 203 + 208 + 209 + 219 + 227 + 230 + 237 = 3119 is prime.

%t Accumulate[Select[Range[800],Divisible[Binomial[2#,#],(#+1)^2]&]] (* _Harvey P. Dale_, Apr 18 2011 *)

%Y Cf. A002503, A065350, A000108, A065344-A065349.

%K easy,nonn

%O 1,1

%A _Jonathan Vos Post_, Apr 15 2010

%E Corrected by Harvey P. Dale, Apr 18 2011.