

A066796


a(n) = Sum_{i=1..n} binomial(2*i,i).


27



2, 8, 28, 98, 350, 1274, 4706, 17576, 66196, 250952, 956384, 3660540, 14061140, 54177740, 209295260, 810375650, 3143981870, 12219117170, 47564380970, 185410909790, 723668784230, 2827767747950, 11061198475550, 43308802158650
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OFFSET

1,1


COMMENTS

Every a(n) is divisible by prime 2, a(n)/2 = A079309(n).
a(n) is divisible by prime 3 only for n=12,30,36,84,90,108,120,... A083096.
a(p) is divisible by p^2 for primes p=5,11,17,23,29,41,47,... Primes of form 6n1. A007528.
a(p1) is divisible by p^2 for primes p=7,13,19,31,37,43,... Primes of form 6n+1. A002476.
Every a(n) from a((p1)/2) to a(p1) is divisible by prime p for p=7,13,19,31,37,43,... Primes of form 6n+1. A002476.
Every a(n) from a((p^21)/2) to a(p^21) is divisible by prime p>3.
a(p^21), a(p^22) and a(p^23) are divisible by p^2 for prime p>3.
a(p^24) is divisible by p^2 for prime p>5.
a(p^25) is divisible by p^2 for prime p>7.
a(p^26) is divisible by p^2 for prime p>7.
a(p^27) is divisible by p^2 for prime p>11.
a(p^28) is divisible by p^2 for prime p>13.
a(p^3) is divisible by p^2 for prime 2 and prime p=5,11,... Primes of form 6n1. A007528.
a(p^31) is divisible by p^2 for prime p=7,13,... Primes of form 6n+1. A002476.
a(p^41) is divisible by p^2 for prime p>3. (End)
Mod[ a(3^k), 9 ] = 1 for integer k>0. Smallest number k such that 2^n divides a(k) is k(n) = {1,2,2,11,11,46,46,707,707,707,...}. Smallest number k such that 3^n divides a(k) is k(n) = (12,822,2466,...}. a(2(p1)/3) is divisible by p^2 for prime p = {7,13,19,31,37,43,61,...} = A002476 Primes of form 6n+1. Every a(n) from a(p^2(p+1)/2) to a(p^21) is divisible by p^2 for prime p>3. Every a(n) from a((4p+3)(p1)/6) to a((2p+3)(p1)/3) is divisible by p^2 for prime p = {7,13,19,31,37,43,61,...} = A002476 Primes of form 6n+1.  Alexander Adamchuk, Jan 04 2007


LINKS



FORMULA

a(n) = A006134(n)  1; generating function: (sqrt(14*x)1)/(sqrt(14*x)*(x1))  Antonio G. Astudillo (afg_astudillo(AT)hotmail.com), Feb 11 2003, corrected by Vaclav Kotesovec, Nov 06 2012


MATHEMATICA



PROG

(PARI) { a=0; for (n=1, 200, write("b066796.txt", n, " ", a+=binomial(2*n, n)) ) } \\ Harry J. Smith, Mar 27 2010
(PARI) a(n) = sum(i=1, n, binomial(2*i, i)); \\ Michel Marcus, Jan 04 2016


CROSSREFS



KEYWORD

nonn


AUTHOR



STATUS

approved



